Unit 10 - angular kinetics

Comparing linear and angular:

1. What do the variables mean in F = m * a? Linear or angular?

2. What do the variables mean in T = I * α ? Linear or angular?

3. Which can we alter in real-time? How?

1. Force = mass * acceleration. Linear inertia.

2. Torque = moment of inertia * angular acceleration. Moment of inertia/rotational inertia.

3. We can manipulate moment of inertia in real-time because it does involves mass and radius unlike linear inertia which juts relies on mass (mass does not change in real-time movements)

1. What is the formula involving linear inertia?

2. What is the formula involving moment of inertia?

3. TRUE OR FALSE: rotational inertia and moment of inertia are the same thing

1. F = m * a

2. T = I * α

3. True

Define moment of inertia

the tendency of body to resist a rotation

how to calculate moment of inertia

I = m * r²

1. Where to put these kids so it is easier to spin (explain using inertia)?

2. Where will putting them make it harder to spin them (explain using inertia)?

1. Putting the kids at the center of the merry-go-round will be easier to spin because you are lowering the moment of inertia. This is because putting them at the center will lower the radius (the torque you need to produce is T = I α, and I or moment of inertia = m * r² of the kids).

2. Similarly putting them on the outside of the merry-go-round will increase their radius —> increase their moment of inertia = they are harder to spin.

note: since is it asking about a spin you should have explained using moment of inertia

Ture or false:

1. In linear motion mass is not proportional to inertia

2. In rotational motion the distribution of mass is the most important part in relation ot inertia

3. the moment of inertia is constant in the human body

1. false

2. true

3. false

1. What axis is this (in relation to inertia)?

2. Flip or spin?

3. Is moment of inertia large or small? WHY?

1. mediolateral axis

2. flip

3. larger moment of inertia because mass is distributed far from axis (r is squared)

1. What axis is this (in relation to inertia)?

2. Flip or spin?

3. Is moment of inertia large or small? WHY?

1. longitudinal axis

2. spin

3. smaller moment of inertia because mass is not distributed far from axis (r is squared)

Is it harder to flip or spin? Explain using moment of inertia

harder to flip because moment of inertia is larger on mediolateral axis because mass is distributed further from the axis so moment of inertia is larger than when spinning

why do you tuck when flipping? explain using moment of inertia

so mass goes closer to axis or rotation (mediolateral axis) and moment of inertia decreases

explain how ice skaters use moment of inertia to jump/spin and to land

arms in when jumping so they can get a faster velocity to spin in the air. tucking arms in decreases radius/distribution of mass so they have a smaller moment of inertia

arms out to land so that they decrease their velocity by making a larger moment of inertia by increasing radius

When gravity is the only force acting on an object (i.e. no contact forces, figure skater jumping to spin with arms tucked in):

1. What is the concept called?

2. What is the equation?

1. Conservation of angular momentum

2. Angular momentum = I * ω

   1. angular momentum = moment of inertia * angular velocity

Angular momentum = I * ω

1. what is this equation for?

2. example of when it is used

1. used for conservation of angular momentum, when gravity is the only force acting on an object

2. figure skater jumping to spin with arms tucked in. ω goes up so I goes down(arms tucked in)

Conservation of angular momentum

1. if you decrease moment of inertia, angular velocity will ____

2. If you increase moment of inertia, angular velocity will ____

1. increase

2. decrease

why do snow boarder crouch down?

see image

How are v = ω * r and moment of inertia related?

increasing radius will increase linear velocity AND moment of inertia, so if you increase radius you will have to work harder to rotate it (more torque bc T = I * α)

Why tell a kid to choke up on a baseball bat?

Less force needed because less moment of inertia due to shorter radius

1. Equation for linear impulse

2. Equation for angular impulse

1. Linear impulse = F * t

2. Angular impulse = T * t

TRUE OR FALSE: Angular impulse does not equal Angular momentum

fasle, Angular impulse = Angular momentum

What equation is this?

T * t = I *ω

Angular impulse = Angular momentum

what equation is this

(F * MA) * t = I *ω

Angular impulse = Angular momentum

explain why 5th is the hardest jump? WHY

5th see image for reasoning idk

1. Explain Torque-Counter Torque

2. Which one of Newton’s laws is it?

1. For every torque exerted by a body segment there is a equal opposite torque exerted on another body segment (about a common axis of rotation)

2. action reaction law

1. explain torque-counter torque using image

2. why do they produce a counter torque?

1. the volleyball player has a larger torque going from shoulder flexion to extension so they extend their legs at the same time to produce a counter torque

2. to prevent the whole body from rotating