Rotational Motion 3

Rotational Motion 3

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Angular Momentum

Recall linear momentum is a measure of how hard it is to

something that is moving.

Linear Momentum = mass x velocity

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The rotational equivalent is angular momentum.
It is a measure of how hard it is to stop something that is

.

Angular Momentum = rotational inertia x angular velocity

 $L=I\omega$  

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Clearly a big wheel spinning fast is ______ to stop than a big wheel spinning slow, and a big wheel spinning is harder to stop than a small wheel spinning at the same speed .

This idea can be extended to find the angular momentum of a point mass. For such a point the _________ ______ is give by I = mr² and ω = v/r so we can derive the following equation on the next slide:

Multiple Choice

The angular momentum equation for a point mass about a given axis of rotation :

• $L=mvr$

• $L=mvr^2$

• $L=mr^2$

• $L=\frac{mv}{r}$

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Conservation of Angular Momentum

“If the net torque is zero, the total angular momentum is conserved"
This means  $L=I\omega$   is constant if   $\tau$  = 0

So, if a spinning ice-skater raises her arms no torque is applied but her angular speed will

Multiple Choice

A spinning bike wheel is held horizontally and it is observed to slow down. Why does this not break the law of conservation of angular momentum?

• Friction causes a torque. Torque causes a change in angular momentum

• It does break the law

• Weight causes a torque to be applied which changes the angular momentum

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Rotational Kinetic Energy

Energy is the ability to do work

Examples of how a spinning object can do work:

windmills, grindstones

Examples of work being done on a spinning object:

disc

, turntable

Multiple Choice

Rotational Energy Equation:

Recall E_k = ½ mv² What is the equation for rotational kinetic energy?

• $E_{kr}=\frac{1}{2}I\omega^2$

• $E_{kr}=\frac{1}{2}I\alpha^2$

• $E_{kr}=\frac{1}{2}\alpha I^2$

• $E_{kr}=\frac{1}{2}\omega I^2$

Multiple Choice

Farica slows a spinning turntable (solid disc) by holding her finger against the edge.

(I = 0.80 kgm² radius = 20 cm. Tangential force = 2.0 N )

The turntable goes from 5.0 rad/s to rest in 10 s.

Calculate the work done by her finger

• 10 J

• 5.8 J

• 12.5 J

• 25 J