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Angular Kinematics

If you shrunk to the size of an ant, and were forced to live on the second hand of a wristwatch, it would behoove you to understand movement in a circle. Prepare for the worst with Angular Kinematics.

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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