test 3 Flashcards
angular position
the orientation of a line with another line or plane SI Unit: degrees/radians
absolute angular position
if the other line or plane is fixed and immovable relative to earth (angle forearm makes with a horizontal plane)
relative angular position
if the other line or plane is capable of moving (angle forearm makes with upper arm)
angular displacement
the change in absolute angular position experienced by a rotating line (angular analog of linear displacement) RHTR SI Unit: rad
flexion of the left knee
negative
extension of the right hip
negative
adduction of the right hip
positive
abduction of the right shoulder
negative
eversion of the left foot
positive
inversion of the left foot
negative
disadvantages of muscle attachment close to a joint
moment arm is short so it takes a large force to create a torque about a joint
advantages to muscle attachment close to a joint
range of motion, longer swing radius, close to axis of rotation, throwing/hitting end are distal (large arc length), faster linear velocity at the end of limb
longer radius = faster linear velocity
why are there staggered starting lines for a 400m track race
relationship between angular displacement and arc length- without a staggered start, runners in the outside lane would end up running further than runners in the inside lane because the radius of the curve they must run is longer
larger radius=larger arc length
angular velocity
SI UNIT: rad/s, degree/s
rate of change in angular displacement (vector quantity)
average angular velocity
how long it takes for something to rotate through a certain angular displacement (divers, figure skaters)
instantaneous angular velocity
how fast something is rotating at a specific instant in time (not how fast swing bat, how fast ball moves when hit)
how do we calculate average linear speed using average angular displacement
arc length= angular displacement x radius, arc length/ time= angular displacement/time, average linear speed= average angular velocity x radius
relationship between instantaneous angular and linear velocity
if instantaneous angular velocity is kept the same and radius is increases, instantaneous linear velocity is also increased
using the instantaneous angular and linear velocity which will have a greater linear velocity- club head or handle
the linear velocity of the club head is faster than the linear velocity of the handle if angular velocity is constant because the club head is further from the axis of rotation
how is the relationship between instantaneous angular and linear velocity used for athletic improvement?
implements such as sticks, clubs, and rackets use the relationship to lengthen the limbs which increases the effective radius
angular acceleration
SI UNIT: rad/s^2, degrees/s^2
rate of change of angular velocity
tangential acceleration
the component of linear acceleration tangent to the circular path of a point on a rotating object (line is tangent) angular acceleration
centripetal acceleration
linear acceleration directed towards the axis of rotation (line directed towards center) linear acceleration; constant angular velocity
does mass or radius of gyration produce and larger increase of inertia
radius of gyration because it is squared so doubling it would actually be quadrupling it
angular inertia
property of an object to resist changes in its angular motion
moment of inertia
quantity that describes angular inertia
can a moment of inertia occur if an object rotates about an axis NOT through its COG? What will this do to the moment of inertia?
an objects moment of inertia about an axis (NOT through COG is larger than its moment of inertia about a parallel axis through the COG
how does a figure skater manipulate her moment of inertia to spin faster
spinning about a longitudinal axis they must adduct their arms to decrease moment of inertia and increase angular velocity
how would a figure skater change her moment of inertia to slow her spin
spinning about a longitudinal axis they must extend their arms to increase moment of inertia and decrease angular velocity
Angular Momentum
SI UNIT: kg•m^2/s (RHTR); the angular analog of linear momentum- quantifies angular motion of an object
Newton’s first law of motion (linear)
everybody continues in its state of rest or of uniform motion in a straight like unless it is compelled to change that state by the forces impresses upon it
Newton’s first law of motion (angular)
angular momentum of an object remains constant unless a net external torque is exerted on it (rigid body: moment of inertia is constant so angular velocity is as well)
why doesn’t gravity have an effect on angular momentum
Because the force of gravity (weight of object) acts through its COG once it leaves your hand and becomes a projectile; the axis of rotation of a projectile is through its COG so gravity cannot create a torque bc the moment arm of the force of gravity is ZERO
Newton’s second law of motion (linear)
the change in motion of an object is proportional to the force impressed upon it in the direction of the force impressed
Newton’s second law of motion (angular)
the change in angular momentum of an object is proportional to the net external torque exerted on it (if this ya the direction of the net external torque)
Newton’s 2nd law for rigid objects
If a net external torque is exerted on an object, the object will accelerate angularly in the direction of the net external torque, and its angular acceleration will be directly proportional to the net external torque and inversely proportional to its moment of inertia
Newton’s 2nd law for non rigid objects
A net external torque acting on a nonrigid object with variable moments of inertia will cause a large and quick change in angular momentum if the net torque is large, and a small and slow change in angular momentum if the net torque is small, provided the torques act for equal time intervals.
what are the 3 items that the change in angular momentum may be seen as? (non rigid)
(1) a speeding up or slowing down of the object’s angular velocity, (2) a change in the direction of the axis of rotation, or (3) a change in the moment of inertia.
what would an object’s angular acceleration be if it’s net external torque was equal to 0 (rigid)
it would also be 0
Newton’s 3rd law of motion (linear)
for every action there is an equal and opposite reaction
Newton’s 3rd law of motion (angular)
for every torque exerted by one object on another the object exerts an equal and opposite torque back on the object
why does a tight rope walker carry a long pole? (3rd)
lower their cog, increase moment of inertia (stability ultimately); to prevent falling moves the pole in the direction of their fall so the pole exerts an equal and opposite torque back on them
relationship between angular impulse and momentum
angular impulse = change in angular momentum
how can a dancer use the angular impulse- momentum relationship to spin
the longitudinal axis of rotation occurs through one foot to the floor and the other foot creates a frictional force that creates a torque, this foot must be some distance from the twisting foot to maximize the moment arm of the torque created
1 oz
23.35g
1 kg
2.2 lbs, 9.81 N
1 inch
2.54 cm
1 yard
.9144 m, 3 ft
1 mike
1609 m, 5280 ft
1 m
100 cm
1000m
1km
