A student sits on a rotating stool holding two 2.9-kg objects. When his arms are extended...

Question:

A student sits on a rotating stool holding two 2.9-kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is 3.0 kg{eq}\cdot {/eq}m{eq}^2 {/eq} and is assumed to be constant. The student then pulls in the objects horizontally to 0.46 m from the rotation axis. (a) Find the new angular speed of the student. (b) Find the kinetic energy of the student before and after the objects are pulled in.

Angular Momentum

Angular momentum is the "linear momentum" equivalent of rotational motion and just like linear momentum, the angular momentum of a rotating object is always conserved unless acted upon by an external torque. The angular momentum, {eq}L {/eq} of an object with a moment of inertia {eq}I {/eq} rotating at an angular speed {eq}\omega {/eq} is

{eq}L=I\omega {/eq}

and its kinetic energy {eq}K.E {/eq} is given by

{eq}K.E=\frac{1}{2}I\omega^{2} {/eq}

Answer and Explanation:

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(a) First we calculate the moment of inertia for when the objects are at {eq}r_{i}=1.0m {/eq} from the axis, call it {eq}I_{i} {/eq}, and also when...

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Conservation of Angular Momentum

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Chapter 7 / Lesson 11
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