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A uniform hoop, disk, and sphere, with t...

A uniform hoop, disk, and sphere, with the same mass M and same radius R, are released simultaneously from rest at the top of a ramp of length L = 2.5 m and angle `theta = 12^(@)` with the horizontal. The objects roll smoothly down the ramp.
What is `v_("com")` for each object at the bottom of the ramp?

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To find the final velocity \( v_{\text{com}} \) of a uniform hoop, disk, and sphere rolling down a ramp, we can use the principle of conservation of energy. ### Step 1: Determine the potential energy at the top of the ramp At the top of the ramp, the objects have potential energy and no kinetic energy since they are released from rest. The potential energy \( U \) can be expressed as: \[ U = mgh \] where \( h \) is the height of the ramp. ...
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