How Does Changing the Radius Affect Angular Speed and Kinetic Energy?

AI Thread Summary
Changing the radius of the rotating objects affects both angular speed and kinetic energy due to the conservation of angular momentum. When the student pulls the objects closer to the axis, the moment of inertia decreases, resulting in an increase in angular speed. The initial angular speed is 0.75 rad/s with the objects at 1.0 m, and the new speed needs to be calculated after they are moved to 0.50 m. Kinetic energy can be determined using the formula KE = 0.5 * I * ω², where I is the moment of inertia and ω is the angular speed. Understanding the relationship between radius, moment of inertia, and angular speed is crucial for solving these types of problems.
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Homework Statement


A student sits on a rotating stool holding two 4.0 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·m2 and is assumed to be constant. The student then pulls the objects horizontally to 0.50 m from the rotation axis.
(a) Find the new angular speed of the student. rad/s
(b) Find the kinetic energy of the student system before and after the objects are pulled in.




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The Attempt at a Solution


Tried working the problem but got stuck with not having the moment of inertia after the weights are pulled in. All of the examples my proffessor worked in class gave us both so i am unsure how to solve for it.
 
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Moment of inertia is typically a function of radius, is it not? All that has changed is the radius of the circle being swept out by the two masses.
 
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Can you calculate the Moment of Inertia for a single point mass a distance 'r' from an axis of rotation?
 
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