Linear Kinetics

Question 1

What is linear kinetics?

Answer 1

Study of the causes of linear motion (i.e., forces acting on or produced by the body)

Question 2

What is a force and what are three things that characterize one? Is it a scalar or vector quantity? Unit?

Answer 2

A push or pull by one object to another. It can change motion (global) or deform an object (localized).

1. Magnitude (W = mg)
2. Direction/line of action (a straight line which travels in the direction that the force is acting through CoM - insertion of a muscle towards its origin, CoM to the center of earth)
3. Point of application (center of the muscle, insertion of a muscle, the point at which the feet and ground are in contact)

Vector quantity

Newtons (N) = kg x m/s^2

Question 3

What are the two types of forces? Provide examples

Answer 3

Non contact: not sensed by the body
1. Gravity - pulls objects with mass towards each other

Fg = G x m1 x m2 / r^2
The force of gravity is inversely proportional to the square of the distance between objects and proportion to the product of their masses - two objects that are far away have a weak force of gravity acting on them and vice versa, the larger the objects the larger the force of gravity

Contact: direct contact with the body
1. Friction
2. GRF
3. Joint reaction forces
4. Muscle forces

Question 4

What is the universal gravitational constant (G)?

Answer 4

6.67 X 10 ^ -11 N-m^2/kg^2

Question 5

What is weight defined as?

Answer 5

The attractive force of the earth on the body

W = Fg = G x m of object - M of earth / r^2

Question 6

What is the force of friction?

Answer 6

A reaction force that occurs when two surfaces in contact attempt to move across each other - occurs opposite to the motion

Ff = µ x FN
Force of friction = coefficient of friction x normal force (equal and opposite to the perpendicular force of gravity, positive)

Question 7

Explain the case of static friction:

Answer 7

In static friction, the frictional force (Fsf) is equal and opposite to the applied force which is why no movement occurs. There will also be no movement if the applied force is less than Fsf.

Fsf = µsf x FN
^maximal friction for the static condition

As you increase the amount of force applied, the force of friction is proportion until motion is reached

Static friction is always greater than kinetic

Question 8

Explain the case of kinetic friction:

Answer 8

Friction is constant and less than maximal static friction

Fkf = µkf x FN

Question 9

Which coefficient of friction is the greatest for any given interaction between two surfaces?

Answer 9

µsf

Question 10

What is a ground reaction force? What is it’s magnitude, point of application, and line of action?

Answer 10

A force that is provided by a surface which one is touching - vector.

Magnitude: walking GRF is 1-1.5 x bw, running GRF is 2-3 x bw
Point of application: at the surface body interface (where an individual is touching the ground)
Line of action: through the center of mass

Question 11

What is a joint reaction force?

Answer 11

Net reaction force acting across a joint surface - force of the proximal bone acting on the distal, and the distal bone acting on the proximal. Not the same as bone on bone force (contact joint force) which requires estimation of muscle force.

Question 12

What is newton’s law of inertia with regards to linear motion?

Answer 12

The law states that an object at rest remains at rest and a body in motion remains in motion unless acted upon by an external force.

ΣF = 0 -> Δv = 0 -> a = 0
ΣF = sum of the forces acting on an object at a particular moment in time

The inertia (resistance force) of an object is directed related to its mass (more mass = more inertia)

Question 13

What is newton’s law of acceleration with regards to linear motion?

Answer 13

Change in motion is proportional to the applied force

If the ΣF is not equal to zero, the motion will proceed in the direction of the net force

ΣF = ma

Question 14

What is linear momentum? How is it related to newtons first law of motion?

Answer 14

Vector quantity of motion - involves two or more objects

p = mv - kg x m/s
More mass an object has, the greater the momentum
More velocity an object has, the greater the momentum

In absence of external forces, the total momentum of a system is conserved
(mv) final = (mv) initial

Question 15

What are the two types of collisons?

Answer 15

1. Elastic: when two objects collide and then separate, velocity of the system is conserved
   m1v1 initial + m2v2 initial = m1v1 final + m2v2 final
2. Inelastic (plastic): when two objects collide and form one mass, system velocity is not conserved
   m1v1 initial + m2v2 initial = (m1+m2) x v final

Question 16

What is linear impulse?

Answer 16

Amount of change in an objects momentum

Δp = ΣF x Δt

Unit of Ns

Question 17

What is the impulse-momentum theorem?

Answer 17

ΣF x Δt= Δp
ΣF x Δt= mv final - mv initial

Impulse = change in momentum

Increasing impulse (a force applied over time) leads to an increased change in momentum

Question 18

What is newton’s third law of action and reaction?

Answer 18

1. For every action, there is an equal and opposite reaction
2. Forces always act in pairs

Question 19

What is a moment? What are the two characteristics of one?

Answer 19

The tendency of a force to cause rotation

1. Magnitude of force (F)
2. Moment arm (d⊥): perpendicular distance from the axis of rotation to the applied force
   *the greater the external moment arm, the more force you are able to generate - can provide a mechanical advantage
   *the greater the internal moment arm, the more force you are able to generate - 90 degrees of elbow flexion

M = Fd⊥
M = Fcosθr

Units of Nm

Question 20

What is the typical moment arm for most muscles?

Answer 20

100 to 105 degrees

Question 21

How do you know the direction of a moment?

Answer 21

Clockwise - negative
Count clockwise - positive

Question 22

With regards to optimal deadlift form, is it better to keep the bar closer to the body or further away?

Answer 22

Closer - shorter moment arm so less force is exerted onto the back, decreasing the risk of injury

Question 23

How does applying a force through the CoG of an object (centric force) or away from the CoG (eccentric force) affect its motion?

Answer 23

1. Force through the CoG, pure translation (Fx is the force causing this)
2. Force a little further from the CoG, some rotation, translation
3. Force even further from the CoG, a lot of rotation (Fy is the force causing this), some translation

Question 24

When is the state of static equilibrium reached?

Answer 24

ΣM = 0
Net moments = 0

Question 25

What is a force couple?

Answer 25

When two forces are acting parallel in opposite directions, creates a pure moment with no translation,only rotation

Question 26

What is moment distribution?

Answer 26

The idea that the maximum moment is generated at the maximum radius, and that the moment decreases as the radius decreases due to the moment arm being smaller

Question 27

What is newtons first law of motion with regards to angular motion?

Answer 27

ΣM = 0
Objects remain in their current state of motion unless acted on by an external force (moment)

Inertia is related to an objects mass and its mass distribution with respect to a given axis of rotation (i.e., more closely mass is distributed to an axis of rotation, the easier it is to change to objects state of angular motion which means that it has less inertia - disc has more inertia than a hoop)
smaller radius = less inertia

Formula 1:
I = Σmr^2
I = Mass moment of inertia
kg x m^2

Formula 2:
I = mk^2
k = radius of gyration which represents an objects mass distribution with respect to a given axis of rotation
k = pl (proportion of radius of gyration as a proportion of length)
I = Mass moment of inertia
kg x m^2
Used when an object is irregularly shaped

Question 28

What is the principal moment of inertia?

Answer 28

Mass moment of inertia with respect to one of the principle axes (anteroposterior, mediolateral, superioinferior)

Question 29

What is the parallel axis theorem?

Answer 29

A way to find the moment of inertia in any location parallel to the CoM axis

I prox = I CoM + mr^2
Kg x m^2

Question 30

What is newtons second law with regards to angular motion?

Answer 30

Law of acceleration, A net moment causes an object to accelerate directly proportional to the moments magnitude and direction

ΣM = Ia

Question 31

How do you calculate angular momentum? How is it related to newtons first law of angular kinetics?

Answer 31

ΣM = H / Δt
H = Iω = mk^2ω
Units: Kg x m^2/s
H = angular momentum

In absence of an external moment, the angular momentum of a system is conserved
H final = H initial
Iω final = Iω initial
mk^2ω final = mk^2ω initial

Decrease inertia, angular velocity increases

Question 32

How do you calculate the angular momentum of a segment (Hs)?

Answer 32

Hs = H local + H remote
H local = Isωs
= moment of inertia about segments CoM x angular velocity about segment CoM
H remote = mdω
= mass of segment x distances from the segments CoM to the bodies CoM x angular velocity of the segment about the bodies CoM

Question 33

How do you calculate angular impulse?

Answer 33

MΔt = Fd⊥Δt = Δh = iω final - iω initial
Units: Nms

Question 34

How do you calculate centripetal acceleration?

Answer 34

ac = vt^2/r = rω^2
Units: m/s^2

Question 35

What is the centripetal force and how do you calculate its magnitude?

Answer 35

Centripetal force is a force that pulls a rotating object towards the center of mass allowing circular motion, known as the center seeking force

(I.e., string of a yoyo, force of gravity, force of friction)

Fc = m x ac = m(vt^2/r) = m(rω^2)
Units: N

Question 36

What is static equilibrium?

Answer 36

Effects of a force at a point in time

If the resultant force and moment acting upon an object is equal to zero
ΣFx = 0
ΣFy = 0
ΣM = 0

Question 37

What is dynamic equilbrium?

Answer 37

Effects of a force over time