What is the ball's linear and angular velocity at the bottom of the hill? Thanks its a physic question?
Wednesday, March 10th, 2010 at
2:21 pm
You are currently browsing comments. If you would like to return to the full story, you can read the full entry here: “What is the ball's linear and angular velocity at the bottom of the hill? Thanks its a physic question?”.
Filed under: Cat Furniture
Like this post? Subscribe to my RSS feed and get loads more!
The way I’d attack this is to argue that the gravitational potential energy the sphere has at the top of the hill will all be converted into kinetic energy of motion and rotation at the bottom of the hill.
So,
mgh = 1/2mv^2 + 1/2 I w^2
Where v is the speed of the center of mass of the sphere at the bottom and w is the sphere’s angular velocity.
I’m assuming that the problem intends that the sphere rolls without slipping. If so the angular velocity and linear velocity are related by
v = wr
Plugging values and solving should get you the answers for v and w, I hope.
One pitfall I almost fell into just now is realizing that h = 5m, not 5m + 0.8m, because even at the bottom the CM of the sphere is still 0.8m above zero height.