Solve the following problems using what you know about
rotation and angular momentum.

Hint: Use radians, meters, kilograms, and seconds or units derived from these for all measurements!

First a little review of rotation:

A 0.35-m diameter grinding wheel rotates at 2,500 rpm. Calculate its angular velocity in rad/s. What is the linear velocity of a point at the outer edge of the wheel? There should be two answers. ωr = v.

A child rolls a ball on a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its diameter? Remember that θr = d.

The tires of a car make 85 revolutions as the car reduces its speed uniformly from 90.0 km/hr to 60.0 km/hr. The tires have a diameter of 0.90 m. What was the angular acceleration? Hint: convert from km/hr to m/s. 1000 m = 1 km. Also, remember that αr = a.

How long would it take for the car in the previous problem to come to a stop if it continued to decelerate at the rate you calculated?

A person exerts a force of 38 N on the end of a door 96 cm wide. What is the magnitude of the torque if the force is exerted perpendicular to the door?

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A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of 1,800 rev/s from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor. Hint: the moment of inertia of a uniform cylinder is I = ½mr^{2}.

Now for some angular momentum problems.

What is the angular momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1,500 rpm? How much torque is required to stop it in 7.0 s? Hint: the moment of inertia of a uniform cylinder is I = ½mr^{2}. There should be two answers to this problem.

A figure skater during her finale can increase her rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate of 3.0 rev/s. If her initial moment of inertia was 4.6 kg· m^{2}, what is her final moment of inertia? How does she physically accomplish this change?

A person stands, hands at the side, on a platform that is rotating at a rate of 8.17 radians/s. If the person now raises her arms to a horizontal position the speed of rotation decreases to 5.03 r/s. In a sentence or two, why does this occur? Mathematically, by what factor has the moment of inertia of the person changed?

Use what you have learned about angular momentum to explain how it is that a bicycle can be balanced upright while moving much better than when standing still.