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# Rotational Inertia & Angular Momentum PowerPoint PPT Presentation

Rotational Inertia & Angular Momentum. Inertia (linear quantity). Symbol Definition Limitations Depends on. m (mass) An object at rest tends to stay at rest and an object in motion tends to stay in motion unless… Acted upon by an outside force Mass ( more mass = more inertia ).

Rotational Inertia & Angular Momentum

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## Rotational Inertia & Angular Momentum

### Inertia (linear quantity)

Symbol

Definition

Limitations

Depends on

• m (mass)

• An object at rest tends to stay at rest and an object in motion tends to stay in motion unless…

• Acted upon by an outside force

• Mass (more mass = more inertia)

### Rotational Inertia (angular equivalent)

Symbol

Definition

Limitations

Depends on

• I

• An object not rotating tends to stay not rotating and an object rotating about an axis tends to stay rotating about that axis unless…

• Acted upon by an outside torque

• Mass distribution (more mass farther from axis of rotation = more rotational inertia)

### Rotational Inertia(I)

• Inertia is a measure of laziness!

• Resistance to the change in rotational

motion

• Objects that are rotating about an

axis tend to stay rotating, objects not rotating tend to remain at rest, unless an outside torque is applied

• A torque is required to change the status of an object’s rotation

### Rotational Inertia (cont.)

• Some objects have more rotational inertia than others

• Objects with mass closer to axis of rotation are easier to rotate, b/c it they have less rotational inertia

• If the mass is farther away from the axis, then object will have more rotational inertia, and will therefore be harder to rotate

### Why does a tightrope walker carry a long pole?

• The pole is usually fairly heavy and by carrying it, he creates a lot of mass far away from the axis of rotation

• This increases his rotational inertia

• And therefore makes it harder for him to rotate/tip over

### Sports Connection

• Running

• When you run you bend your legs to reduce your rotational inertia

• Gymnastics/Diving

• Pull body into tight ball to achieve fast rotation

### Other Examples:

Splash!

Time Warp: Optimal Dive

Spinning in zero Gravity

### The big idea

• Rotational Inertia depends on mass and radius

• If either one of these is large, then rotational inertia is large, and object will be harder to rotate

• Different types of objects have different equations for rotational inertia

• But all equations have m and r2 in them.

### Momentum

Symbol

Definition

Equation

Conservation

• p

• Inertia in motion

• Momentum = mass x velocity (p=mv)

• If no unbalanced external force acts on an object, the momentum of that object is conserved

### Angular Momentum

Symbol

Definition

Equation

Conservation

• L

• Inertia of rotation

• Angular momentum = rotational inertia x rotational velocity (L = I )

• If no unbalanced external torque acts on a rotating system, the angularmomentum of that system is conserved

### Conservation of Angular Momentum

• If no outside torque is being applied, then total angular momentum in a system must stay the same

• This means, if you decrease radius, you increase rotational speed

• Increase radius, then rotational speed decreases

I – represents rotational inertia

ω -represents angular speed

### Angular Momentum

• The more rotational inetia has (the more mass farther out from the center) and the higher the rotational velocity, the more angular momentum it has. Example:

### Examples:

• Helicopter tail rotor failure

• Tail rotor failure #2

### Sports Connection…

• Ice skating

• Skater starts out in slow spin with arms and legs out

• Skater pulls arms and legs in tight to body

• Skater is then spinning much faster (higher rotational speed)

• Gymnastics (pummel horse or floor routine)

• Small radius to achieve fast rotational speed during moves, increase radius when low rotational speed is desired (during landing)

### Do cats violate physical law?

• Video

• They rotate their tail one way, so that their body rotates the other so that their feet are facing the ground and they land on their feet.

• This combined with their flexibility allow them to almost always land on their feet

### Universe Connection

• Rotating star shrinks radius…. What happens to rotational speed??

• Goes way up….. Spins very fast

• Rotating star explodes outward…. What happens to rotational speed??

• Goes way down … spins much slower

### Applications…

• The Big Cheese!

• The Gyrowheel