Quiz 3 Flashcards
Gravity causes a projectile to move in a (blank) path that is symmetric about the (blank)
parabolic
apex
What are the 2 different types of projectile motion?
1. Object acting as projectile
(Basketball, baseball, football, shot put, hammer, discuss, javelin, volleyball, tennis ball, arrow (archery)
(High jump, long jump, gymnastics, figure skating, diving, ski jumping)
What are the 3 main variables we manipulate in projectile motion?
- Flight distance
- Flight time
- Maximum height
Why do we always break the motion into X and Y components (displacement, velocity, acceleration)?
- Because they are INDEPENDENT
- Because the vertical component is influenced by gravity (x) and the horizontal(y) component is not à Allows us to use different equations
- both are vectors.
Takeoff velocity often given as projected (blank) with corresponding (blank)
(ie. Ball was projected at 10 m/s at 30° to the horizontal)
vector
angle
What are the 2 perpendicular components of a velocity?
Vx = horizontal component
Vy = vertical component
If the angle between 2 known-length vectors is (blank), you can use pythagorean theorem to find your unknown
90 degrees
What is the formula for pythagorean theorem?
R2 = P2 + Q2
(blank) = Longest side but shortest distance
between x and y points
hypoteneuse
sin = (blank)
cos = (blank)
tan = (blank)
opp/hyp
adj/hyp
opp/adj
Remember that the motion of a body is influenced only by (blank) (in the vertical direction).
Therefore the ONLY acceleration that the body experiences is a vertical acceleration due to gravity of (blank) in the (blank) direction
gravity
9.81 m/s2
downward
Horizontally, (blank) must be zero, since no forces act in this direction (ignore air resistance)
SO… Equation for constant (blank) applies
sfx = six + vixt
- Where sfx and six are the (blank) and (blank) displacements in the x direction
- vix is the initial and (blank) velocity in the x direction
- t is the time component
acceleration
horizontal motion
final
initial
constant
Equations for vertical component of projectile motion:
Use the equations for constant acceleration, replacing (blank) with (blank) (-9.81 m/s2)
a
g
What are the 3 factors that influence projectile trajectory?
Projectile angle
Projectile speed
Relative height of projection
(projection height - landing height)
What is the optimal angle of projection for the most distance?
45 degrees
How are 15/75 degree and 30/60 degree projection angles related?
They will have the same horizontal distance as they have the same difference between them and 45 degrees
How does projectile speed affect horizontal distance?
An increase in speed results in an increase in object displacement, assuming the same projection angle
Angle of projection θ dictates magnitude of the X and Y components.
angle < 45 then (blank)
angle = 45 then (blank)
angle > 45 then (blank)
Vx > Vy (X bigger)
Vx = Vy (same)
Vx < Vy (Y bigger)
Relative projection height :
difference between (blank) height and (blank) height
projection
landing
*Relative projection height = 0
(Release = Landing)
* (blank)
* (blank)
soccer
golf drive on level ground
*Relative projection height > 0
(Release lower than Landing)
* (blank)
* (blank)
golf shot onto elevated green
basketball free throw
- Relative projection height < 0
(Release higher than Landing) - (blank)
- (blank)
soccer throw in
shotput
What is the best projection angle for maximum height?
90 degrees
Relative projection height greater than 0
optimal projection angle of (blank)
less than 45 degrees
Relative projection height equal to 0
optimal projection angle of (blank)
45 degrees
Relative projection height less than 0
optimal projection angle of (blank)
greater than 45 degrees
What is the optimal angle for maximum projection speed?
45 degrees
If Hprojection = 0 (ie. Hrelease = Hlanding)
the optimal release angle is (blank)
45 degrees
Horizontal velocity is determined by
1. (blank)
2. (blank)
projection speed
projection angle
Vertical velocity is determined by
1. (blank)
2. (blank)
projection speed
projection angle
Maximum height is determined by
1. (blank)
2. (blank)
vertical velocity
projection height
Flight time is determined by
1. (blank)
2. (blank)
3. (blank)
vertical velocity
projection height
final height
Flight distance is determined by
1. (blank)
2. (blank)
horizontal velocity
flight time
(blank) axis (Sagittal plane):
divides the body into left and right halves
(blank) axis (Frontal plane):
divides the body into front and back halves
(blank) axis (Transverse plane):
divides the body into top and bottom halves
mediolateral
anterioposterior
vertical
What are 3 ways to measure angular displacement?
Can be measured using
*Revolutions (r)
*Degrees (deg)
*Radians (rad)
What are two scenarios where revolutions are used as a measurement of angular displacement?
Used in sport description
- Diving/Gymnastics/Figure Skating
* full twisting one and a half
* inward two and a half
2.Cycling
* rpm
What is the ratio of a degree to a revolution?
what are 3 uses of degree as a measurement?
Smaller unit (1/360th of a revolution)
Widely used in everyday life and sport
1. loft of the club
2. angle of release
3. segment description
How big is a radian compared to a degree?
What is the definition of a radian?
Much smaller value than degrees
Radian: Ratio of arc length to the radius of circle
What is the equation for a radian?
Theta = s/r
Where:
Theta = angle
s = arc length
r = radius
if arc length (s) = length of radius (r)
then angle (ϴ) = 1 radian
The number of radians in a semicircle = (blank)
The number of degrees in a semicircle = (blank)
Therefore 1 rad = 180 deg/π = (blank)
pi
180
57.3 degrees
Knowing that the circumference of a circle is:
*(blank) degrees
*(blank) rad
*(blank) revolution
360
2
1
What is the angular displacement of 96 degrees expressed in radians
1.675
Express a displacement of 0.82 radians in degrees
46.986
What is the equation for angular velocity?
ω = Δϴ/ Δt = (ϴf - ϴi ) / ( tf - ti )
ω = angular velocity (omega)
ϴ = angular displacement in radians
∆t = time interval in seconds
What is the equation for angular acceleration?
α = Δω / Δt = (ω f - ω i ) / ( tf - ti )
α = acceleration (alpha)
ω = angular velocity in radians/second
Δt = time interval in seconds
A figure skater performs a triple twisting jump. She rotates around her longitudinal axis three
times while she is in the air. The time it takes to complete the jump from takeoff to landing is
0.8 seconds. What was Michelle’s average angular speed in twisting for this jump?
(blank) rev/s
(blank) degree/s
(blank rad/s
3.75 rev/s
1350 degree/s
23.6 rad/s
ω= ∆θ/ ∆t
ω = 3revs/0.8sec
ω = 3.75rev/s
Or
ω = 1080º/0.8sec = 1350º/s
Or
ω = 18.8rad/0.8sec = 23.6rad/s
What is the angular acceleration of a person who increases her angular velocity from 5.50 to 9.00 rad/s in 3.00s?
(blank) rad/s2
1.167 rad/s2
α = 9.0-5.5 / 3.0
α =1.167 rad/s2
Many sports use angular (blank) to increase the linear (blank) of an implement:
ie., hammer throw, discus, golf, baseball, almost any projectile activity
motion
velocity
The (blank) the radius of rotation (r), the (blank) the linear distance or arc distance (s) travelled by a point on a rotating body.
larger
greater
What is the equation for linear displacement?
s=(r)(theta)
where:
*s = linear displacement of the point of interest
*r = radius of rotation
*theta = angular displacement of the rotating body
(MUST BE in radians (57.3 degrees)
A baseball player swings a bat at a fast ball. Consider the handle of the bat where the hands grip it to be the fulcrum. The bat is 0.5m from the handle to the top of the bat. The start angle of the swing is 170º and the angle at which the ball is hit is 90º.
A. What is the angular distance traveled by the bat?
B. What is the linear distance traveled by the end of the bat?
A.
Angular distance (ϴ) = 170̊– 90̊ = 80̊
Change 80 deg to rad = 1.40
B.
s = (r)(theta)
s = 0.5*1.40rad
s=0.7m
Instantaneous linear velocity occurs at a (blank) to the circular path of the point.
tangent
§If the object was released from its (blank) motion, it would travel on a tangent
line from that point out with an initial linear (blank).
angular
velocity
If the object was released from its (blank) motion, it would travel on a tangent
line from that point out with an initial linear (blank).
angular
velocity
The relationship between linear and angular velocity can be described by the following equation?
v = r.ω
Where
*v = linear velocity
*r = distance from centre of rotation
*ω = angular velocity
This relationship describes how a point that is rotating at ω radians / second at a distance of r metres from it’s centre will possess a linear velocity of v metres per second.
Axis system used to define the direction of the velocity of the object.
*Radial axis:
–(blank) at object’s position
–Directed (blank) from centre of circle
–Radial velocity is (blank) on a circular path (radius is constant)
*Transverse axis:
–Rotated at (blank) to radial axis
–Transverse velocity = (blank) * (blank)
(vT) =(ω) *(r)
origin
away
zero
90 degrees
angular velocity * distance from center of rotation
*Angular acceleration can be broken down into
(blank) and (blank) components
transverse
radial
Transverse acceleration of a body due to
it’s angular acceleration along a circular
path is defined using the following
equation:
aT = r.α (m/s)
Where:
aT = transverse acceleration of the object
r = distance from centre of rotation
α = angular acceleration
To create angular motion, a force is applied to an object such that the force does not pass
through the object’s centre of mass
This kind of force is called a (blank)
moment of force
moment of fource allows measurement of a muscle’s ability to cause (blank) about a joint
The moment of force is the same as (blank)
What is the formula for moment of force?
rotation
torque
M = Fd
Moment is defined mathematically as the force times perpendicular distance to the axis of rotation
Moment of Force can be defined in relation to Newton’s second law:
(blank)
law of acceleration
A body’s angular motion will change when the moment of force applied is non-zero.
What is the formula for moment of force in relation to acceleration?
MR = ƩMa = Iaα [Nm]
Where
*MR and ƩMa represent the magnitude of the resultant moment of force acting on the body about axis a
*Ia represents the moment of inertia of the body [kg.m2] about axis a
*α represents the angular acceleration [rad.s2]
(blank) refers to the reluctance or resistance of an object to change its angular motion
moment of inertia
moment of inertia (I) of an object (blank) as its mass (m) (blank)
increases
increases
moment of inertia varies with (blank) distribution of the object
(i.e. more concentrated the mass is about the (blank), the lower the moment of inertia)
mass
axis
moment of inertia varies with the axis of (blank)
(i.e. as m moves farther away from an axis of rotation, I will increase as the square of the displacement, or moment, from that axis)
rotation
What is the formula for moment of inertia?
I = (sum of )m * r(squared)
*I1=m1 * r1(squared)
*I2=m2 * r2(squared)
*I3=m3 * r3(squared)
What is the moment of
inertia for this 1.2kg bat?
Given Quantities
m1 = .6 kg r1 = .8 m
m2 = .4 kg r2 = .5 m
m3 = .2 kg r3 = .3 m
0.502 kg * m2
Moment of Inertia (I) in a human body:
Real bodies are not (blank) masses (or even solid baseball bats)
Body mass is spread out along a (blank)
The mass has a shape that is (blank)
Radius of (blank), k - distance that represents how far away from the axis of rotation a body’s mass is distributed
* (blank) K – mass is spread away from the axis
* (blank) K – mass is packed close to the axis
point
radius
non-uniform
gyration
large
small
Radius of Gyration (k)
Is a measure of the spread of mass about an axis of (blank)
rotation
Radius of gyration:
»Not the same as the segmental centre of gravity (CG)
»(blank) of k changes as the axis of rotation changes
»It is only defined with respect to a (blank) axis of rotation
»Most tables will give ‘k’ for relevant axes
size
specific
What is the formula for moment of inertia around an axis of rotation?
I = mk2
»k = radius of gyration (m)
»m = mass (kg)
»Units (kg∙m2)
I = mk2
What happens when you double m?
Double m - Double Rotational Inertia
I = mk2
What happens when you double k?
Double k – Quadruple Rotational Inertia
A (blank) can
–Rotate about different axes (3 usually)
–Have different moments of inertia depending on axis
–But only one 1 per axis
rigid object
*Humans are (blank) allowing them to:
–Change mass distribution about an axis
–Change moment of inertia about that axis
–Have more than one 1 per axis
non-rigid
What are 3 examples of humans manipulating their moment of inertia?
Figure skater, diver, gymnast
Radius of Gyration changes with (blank) distribution
mass
Forearm = (blank) rotational axes = (blank) different radius of gyration
(blank) changes with axis of rotation
2, 2
k
(blank) increases as mass moves away
from axis of rotation – arms up
in spin; legs out to slow down
and come out of spin
moment of inertia
What is the moment of Inertia of the Forearm at the elbow?
At the elbow:
–Radius from proximal end
–52.6% of 30cm = 15.8cm
–Mass of forearm = 1.12kg
0.028 kg.m2
I = mk2
I = 1.120.1582
I = 1.120.025
I = 0.028kg.m2
What is the moment of Inertia of the Forearm at the wrist?
At the wrist:
–Radius from distal end
–64.7% of 30cm = 19.4cm
–Mass of forearm = 1.12 kg
0.0421 kg.m2
I = mk2
I = 1.120.1942
I = 1.120.038
I = 0.0421kg.m2
Angular impulse increases by:
(blank)
(blank)
*Increased moment of force (M)
*Increased duration of application M(t)
(blank) is defined as
*the time integral of the resultant moment of force applied to the body
OR
*The area under the resultant moment of force time history
angular impulse
What is the formula for angular impulse?
=(sum of) Mr * dt
or
=(sum of) (rFsin(theta))dt
Where:
Mr is the resultant moment of force
F is the resultant force
r is the distance from the centre of gravity of the object to the point of application to the
force
ϴ is the angle between r and F
dt is the time interval of the applied force
If the force or moment of force applied is (blank), then the
amount of impulse of a moment of force can be defined as the
magnitude of the constant moment of force times the duration of the force
The formula is?
constant
=Mt
=Fdt
Where
§M is the constant moment of force
§t is the duration of the impulse
§F is the constant force
§d is the perpendicular distance between the force’s line of action and the axis of rotation
What is the angular impulse produced by a hand crank that is producing a torque of 35.8 Nm for 5.00 minutes?
179 kg . m2
(blank) is defined as the product of the body’s moment of inertia about its centre of gravity in kilogram metres squared, times it’s angular velocity in radians per second.
angular momentum
What is the formula for angular momentum?
angular momentum = L = lcgw
Angular momenta are (blank) that possess both a magnitude and direction
Use the (blank) rule to determine directionality
vectors
right hand
Just like linear impulse and momentum, (blank) Impulse and Momentum are related
What is the unit?
angular
Units: kg.m2/s or N.m.s
(blank) occurs when the resultant force acting on a body is centric (through the body’s centre of gravity) and there are no external moments of force
Conservation of angular momentum does NOT mean that the body’s angular motion is (blank)
Conservation of angular momentum
constant
A (blank) body cannot change its moment of inertia but a multi-segment body can
(ie. human body)
If the net moment of force applied to a system equals (blank), the system’s angular momentum (about a fixed axis of rotation or about the body’s centre of mass) remains constant
rigid
zero
What is the formula for conservation of angular momentum?
If (sum of )M = 0, then L = lcgw = constant
If (sum of)M = 0, then LinitialWinitial = LfinalWfinal
Where L is angular momentum
Icg is moment of inertia about centre of gravity
ω is angular velocity in radians / second
*(blank) (I) changes as the body segments change position
*(blank) (w) changes to compensate for the change in moment of inertia (I)
moment of inertia
angular velocity
Angular momentum is (blank)
–Angular momentum about (2) axes (somersaulting & twisting)
can be altered
–Transfer angular velocity from one axis to another
constant
2
Angular velocity may be (blank) between axes in the air
*(blank) sum of the two must remain constant in magnitude and direction
transferred
vector
What are 2 examples of transfer between axes?
*Asymmetrical arm movements
*Rotation of the hips(termed hula movement)
*These movements tilt the axis of rotation out of the original plane of motion
The angular momentum in a body stays constant in the absence of (blank) torques:
What is an example of this?
external
Ex. Diving:
Somersaulting angular momentum changes to twisting angular
momentum
*Angular momentum
–Can be transferred from one (blank) to another
–Can be transferred from one (blank) to another
*Conservation requires:
–The momentum leaving one plane must be associated with (blank) in another plane by an (blank) amount
plane
axis
increase
equal
Strategy: Asymmetrical arm movement
*Create twist from somersault - (blank) right arm
*To stop twisting – resume a (blank) position
drop
symmetrical
Volleyball Spike
*Initial (blank) momentum = 0 (ie. linear jump upwards)
*Move hitting arm with high angular (blank) and angular (blank)
*Compensating (blank) of lower body with equal L in opposite
direction
angular
velocity
momentum
rotation
What are the 5 types of movement through water and air?
- Buoyancy
- Drag
- Lift
- Magnus effect
- Principle of Spin
What are the 4 forces acting on a swimmer?
Weight is going down
Buoyancy is going up
Thrust is going forward
Drag is going backward
What is the definition of buoyancy?
buoyancy s the vertical force supporting an object in a fluid
What is archimedes’ principle?
” a body partially or fully immersed in fluid will be buoyed up by a force equal to the weight of the fluid displaced by the body”
this is the reason why a heavier-than-water object floats
(ex. ship’s bottom has a large area therefore will displace more water, ship will descend until the buoyant force is equal to the vessel’s weight
used to indirectly measure density
What is the formula for density?
What is the unit for density?
p=m/v
p=density
m=mass
v=volume
(kg/m3)
What is the density of water at room temperature?
What is the density of air?
Are muscle, bone and fat denser than water?
Are bodies uniformly dense?
1000 kg/m3 at room temperature (0 degrees)
1.29 kg/m3
muscle and bone are denser than water, but fat is less dense than water
bodies aren’t uniformly dense but are assumed to be
What forces increase with depth?
What is the result of these increased forces?
What is buoyant force?
What direction does it act in/
What is the center of buoyancy?
What is the displaced fluid’s weight equal to?
What is the equation for buoyant force?
external forces
resultant is a vertical force through the center of volume called the center of buoyancy
buoyant force is force equal to the weight of the fluid displaced by a submerged body
the direction is vertical through the center of volume (AKA center of buoyancy)
displaced fluid’s weight is equal to fluids volume times its density times g (9.81 m/s2)
Fbuoyant = volume x density x 9.81
What is the definition of relative density?
density of one body relative to the density of water (or a fluid medium)
denser bodies sink, less dense bodies float
relative density greater than 1 = sink
relative density less than 1 = float
What happens when center of buoyancy and center of gravity are different?
When center of volume/buoyancy and venter of gravity are misaligned, a moment of force is created that could tip the boat
What do flotation devices create?
flotation devices should create a moment of force to bring the head to the surface and the mouth out of the water especially when the person is unconscious
What are the 3 types of drag for swimmers?
1) form drag (pressure difference between the front and back of
the swimmer) “pressure difference”
2) wave drag (the resistance of a wave) “pushing water”
3) surface drag (body surface and water molecules) “friction”
What is the formula for pressure?
What is the unit?
What is the average air pressure at sea level?
How much pressure is created by 1 pascal?
Are pascals or kilopascals more commonly used?
P = F/A = force/area
the units are pascals (Pa) or kilopascals (kPa)
101.325 kPa
1 pascal is the pressure created by a 1 newton force applied to 1 square meter
Since this is a relatively small pressure, kilopascals are more commonly used
What is the cause of form drag?
What is the formula?
What are 2 ways we reduce form drag?
due to turbulent flow around an object
Ffd = (-1/2Cdrag)(p)(An)(v2)
Cdrag = drag coefficient
p = fluid density
An = surface area perpendicular to motion
v = velocity through fluid
Streamlining reduces turbulence and drag
Decreasing frontal area is also an important factor but minimizing changes in velocity is important
What is the cause of wave drag?
What creates a bow wave?
due to interaction between two surfaces of different viscosity
(ex. bow wave)
An object moving along the surface of water will create a bow wave. Work is required to lift the water and thus slow the motion. This is the reason why swimming underwater is easier. The amount of this drag depends upon the shape of the leading edge.
What is the cause of viscous or surface drag?
What is the formula for surface drag?
due to interaction of molecules moving past each other at the boundary layer at slow velocities
(ex. when flow is laminar-Stoke’s law)
Fvd = (-6) (pi) (r) (n) (v)
r=radius of sphere
n=viscosity of fluid
v=velocity through fluid
Are swimmers faster underwater or above water?
underwater, no wave drag
Does pulling or sitting in create more watts in cycling?
pulling
What is bernoulli’s principle about lift?
What is the formula for bernoulli’s principle?
lift force on an air foil may be explained by bernoulli’s principle
higher air flow on top of wing reduces pressure producing a lift force (Bernoulli)
Flift = (Clift) (p) (Ap) (v2)
Clift = coefficient of lift
p = fluid density
Ap = area parallel to velocity
v = relative velocity of air foil
What is the relationship between lift and drag?
Angle of attack changes relationship between lift and drag
Too steep creates excessive drag
Not steep enough reduces lift
What is the magnus effect caused by?
possibly due to bernoulli principle or turbulent flow around roughly surfaced object
roughness can be caused by laces (baseball), dimples (golf ball), wear (table tennis) or nap (lawn tennis)
What are 4 things that are an example of the magnus effect?
Magnus effect
* Distance
* Golf
* Curve ball
* Soccer
What are 2 things that have an unpredictable trajectory?
Unpredictable trajectory
* Knuckle ball
* Volleyball serve
What are 2 things that have a predictable trajectory?
Predictable trajectory
* Fast ball
* Football
What are 3 things that have rebound control?
Rebound control
* Basketball pass
* Basketball shot
* Golf (putting backspin on the ball)
What is the relationship between spin and a volleyball serve?
No spin and slow velocity creates an unstable
and unpredictable trajectory
A minor wind gust will disturb the trajectory as
will an imbalance in the ball
Which sport has equipment that helps deal with friction?
In football, players use gloves as a means to help control the ball, particularly when making catches. In order to develop better gloves, an understanding of how materials actually adhere (stick) to each other is required. Scientists are constantly searching for new and innovative ideas for adhesive substances. Often, new
substances are modeled after examples found in nature. In 2008, a group of scientists developed an adhesive material modeled after the foot pads of the gecko.
What are examples of lift force in sport?
Discus
What are the 4 tenets of movement analysis?
- Describe the task (anatomical description).
- Identify the critical features and provide teaching clues
* critical features – teaching/intervention cues. - Use the Movement Principles to break down and describe
the task
* range of motion, coordination, segmental interaction, force – motion, force-time, inertia, balance - Use biomechanical principles to describe the strategy you
used to identify the critical features and movement principles of the task.
* muscle actions, linear and angular kinematics, mechanics of the musculosketal system, muscle kinetics, fluid mechanics, projectiles.
What are the 4 main training principles?
- Specificity
-Range of motion, specific to the joint(s)
-Strength
-Speed of contraction (atp-cp, mitochondrial) (15 sec reps)
-Type of contraction - Over load
-Increasing resistance
-Increasing reps
-Increasing load of range of motion - Adaptation/Recovery
-Energy systems
-hypertrophy - Recovery/Detraining
What is the difference between stabilizing and destabilizing forces at a joint?
destabilizing force works perpendicular from the bone
stabilizing force works parallel to the pone
What are 4 uses for EMG?
- Myopathies or Neuropathies diagnosis
- Muscle onset/offset (activation detection)
- Force/EMG relationship
- Fatigue Index
