Velocity of the Center of Mass

AI Thread Summary
A spherical shell of mass 1 kg and radius 2.0 cm is released from a height of 1.00 m on an incline, and the task is to determine the velocity of its center of mass at the bottom. The relevant equations include rotational kinetic energy, potential energy, and translational kinetic energy. The discussion emphasizes the importance of using variables to represent unknown parameters, particularly when the angle of the incline is not provided. A suggested approach is to manipulate the formula for rotational kinetic energy to eliminate terms like moment of inertia and angular velocity, simplifying the energy equations. The participant successfully navigated the problem, indicating progress in understanding the concepts involved.
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Homework Statement


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A shperical shell of mass = 1kg and radius 2.0cm is released from rest at the top of an inclined plane at a height of 1.00m. The ball rolls down the incline without slipping, what is the velocity of the center of mass at the bottom of the incline.

Homework Equations



I'm assuming it will be using

KE rotational, which is 1/2 IW^2
Potential Energy which is mgh
KE translational which is 1/2 mv^2
tangential acceleration: at= αR

The Attempt at a Solution



I have no idea where to begin. If we were given the angle of the incline, this would be much easier, but we are not.
 
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If you do not know the value of a parameter, leave it as a variable. HINT: use r for the radius of the ball.

Now see if you can manipulate the formula for rotational kinetic energy to eliminate "I" and "omega" leaving only m, r and v. The goal is to have a single formula for total energy with only a few unknowns in it (ideally only one).
 
I got it, thank you!
 
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