# 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}

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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... 