Classical Mechanics

Angular Kinematics

Applying angular kinematics

         

The wheels of a bicycle spin with an angular speed of 720 rad/min. 720 \text{ rad/min} . The cyclist applies the brakes causing uniform deceleration, and after 2 s2\text{ s} of deceleration, the wheels are spinning at 360 rad/min. 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 cm r= 50 \text{ cm} moves forward with a linear speed of 9 m/s. 9 \text{ m/s}. What is its angular speed?

The moment of inertia of a turbine in a jet engine is 7 kgm2. 7 \text{ kg} \cdot \text{m}^2. It is accelerated uniformly from rest to an angular speed of 15 rad/sec 15 \text{ rad/sec} in 5 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 m 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 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 m/s2. g= 10 \text{ m/s}^2.

A figure skater is spinning with an angular velocity of +14 rad/s. +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 rad. + 15 \text{ rad}. Determine the approximate magnitude of her angular acceleration.

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