# Angular Kinetics

What is angular motion?

rotation around an axis

What is angular kinetics

study of torque produced by force and its effects on the objects angular motion

What is the formula for Torque when applying it to angular motion

ET(Torque) = I(moment of Inertia) x a(angular acceleration)

What does the toque of an angular motion depend on

Moment of Inertia and angular acceleration

What is the Radius of Gyration (k)?

-The distance from the axis at which the mass of a body maybe assumed to be concentrated
-A value that represents how the mas of the object is distributed from the axis

The further the mass from the axis....

the greater the radius of gyration

Why does tucking the knees and arms closer to the body decrease radius of gyration (k)?

It brings more of the bodies mass closer to the axis of rotation

Why does lifting the arms laterally INCREASE radius of gyration (k)?

It brings some of the mass of the body AWAY from the axis of rotation

Which plane has a longer radius of gyration (k), longitudinal axis(sagittal or left and right) or medial/lateral axis? Why?

The medial/lateral axis is longer because humans are more longer than we are wider

What is moment of Inertia (I)?

Property of an objects resistance to change in angular motion

Greater Inertia equals.....

Greater resistance to change

What is the formula for Moment of Inertia (I)?

mass (M) x Radius of gyration^2(k^2)

What does moment of inertia depend on?

mass of the object and its radius of gyration

What plane has the highest moment of inertia?

Frontal plane (anterior/posterior axis)

How do athletes spin faster?

By manipulating there bodies to decrease change in angular motion to spin faster

sprinters vs distance runners

Sprinters use "heel to butt" to decrease the radius of gyration at the hip to increase speed
Distance runners do not because it is not energy efficient but may still have less inertia depending on the mass of the person

What does "choking the bat" in baseball mean and why is it used?

It means bringing the hands higher on the bat to decrease radius of gyration and inertia and take better control of the bat

What is angular momentum?

the quantity of rotation of a body, which is the product of its moment of inertia and its angular velocity.

What is the formula for angular momentum (H)?

Inertia (I) x Angular velocity (w)

What does angular momentum depend on?

The inertia and the angular velocity

What is angular impulse?

Sum of all torque over a period of time

What is the formula for angular impulse?

Net Torque (ET) x Duration of torque applied (t)

Why do tennis players pull there rackets back before hitting a ball?

It increases the amount of torque being used and the time it is under rotation with increases the angular impulse

What is the law of conservation

If the change in torque or angular velocity is 0, then it will be conserved

What happens to a figure skater when crossing her arms when referring to angular velocity, momentum and torque?

When crossing the arms the radius of gyration decreases because the mass of the body is now closer to the line of axis. The torque is conserved and the velocity increases which causes causes the inertia to decrease to conserve the momentum

What happens to a figure skater if she extends her arms to the side when referring to angular velocity, momentum and torque ?

Radius of gyration then increases which increases the moment of inertia which causes velocity to decrease to conserve the momentum

What is law of acceleration?

When t he torque does not equal zero, the object will accelerate in the direction of the torque

What is the formula to find the angular acceleration?

angular acceleration (a)= Torque (ET) / Inertia (I)

Angular acceleration is proporortial and inversely proportional to...

..Proportional to the torque and inversely proportional to the inertia

What does the law of acceleration analyze and not analyze?

Law of acceleration can analyze torque and acceleration of a specific times.
It cannot analyze effects of torque over time

What can analyze the effects of torque over time?

Angular impulse-momentum relationship

Angular impulse is equal to...

the change in angular momentum

What is the formula for the relationship between angular impulse and momentum?

Angular impulse (Torque x Duration) = Change in Angular momentum (Inertia (I) x (change in velocity (w^f-w^i))

How to golfers use the angular impulse-momentum relationship?

Swinging the club overhead first and then down increases torque and the duration of the swing which in turn increase the velocity which then increase the momentum

How does a baseball player use the angular impulse-momentum relationship to decrease momentum?

He continues to swing the arm after the ball leaves the hand

Change in velocity is proportional and inversely proportional to...

Proportional to the Impulse (Torque and duration) and inversely proportional to the inertia (I)

What is the law of reaction (Newton's 3rd law)?

for every action, there is an equal and opposite (paired) reaction

What do the effects of torque depend on?

Moment of inertia

Are the magnitude of torque and effects of the torque of a moving object the same?

No. The magnitude is the opposite directions are the same but the effects are not

If a long jumper is folding there body to jump, are the magnitude of the legs going towards the trunk the and the torso going towards the legs the same? Does that also mean their accelerations are the same?

The magnitude of the torso and legs are the same.
But if the Moment of inertia for legs and torso are different then the acceleration is not the same