Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A solid sphere is let go from rest at the top of a slope at , long, and rolls without slipping. Taking , find its acceleration, the time it takes, and its speed at the bottom.
Rolling without slipping: . Kinetic energy: . Down a slope: and ; static friction does no work.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Acceleration. .
Step 2. Time. .
Step 3. Speed. .
Answer: , , .
Check. Energy: the drop is , and . Same.
Watch out. The sphere is slower than a sliding block (): part of its energy goes into spinning.
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