Classical Mechanics

# Applying angular kinematics

The wheels of a bicycle spin with an angular speed of $720 \text{ rad/min} .$ The cyclist applies the brakes causing uniform deceleration, and after $2\text{ s}$ of deceleration, the wheels are spinning at $360 \text{ rad/min}.$ From the moment the brakes are applied, how long will it take for the bicycle to come to a complete stop?

A tire with radius $r= 50 \text{ cm}$ moves forward with a linear speed of $9 \text{ m/s}.$ What is its angular speed?

The moment of inertia of a turbine in a jet engine is $7 \text{ kg} \cdot \text{m}^2.$ It is accelerated uniformly from rest to an angular speed of $15 \text{ rad/sec}$ in $5$ seconds. Find the magnitude of net torque required.

At the local swimming hole, a favorite trick is to run horizontally off a cliff that is $80 \text{ m}$ above the water, roll yourself up into a "ball", and rotate on the way down to the water. If the average angular speed of rotation is $2$ revolutions per second, what is the total number of revolutions during the fall?

The air resistance is negligible, and the gravitational acceleration is $g= 10 \text{ m/s}^2.$

A figure skater is spinning with an angular velocity of $+14 \text{ rad/s}.$ She then comes to a stop with a constant deceleration over a brief period of time. During this time, her angular displacement is $+ 15 \text{ rad}.$ Determine the approximate magnitude of her angular acceleration.

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