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knowlewj01
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A uniform sphere is rolling without slipping on a horizontal surface at 2m/s. It then rolls without slipping up a hill to height h, where it briefly comnes to rest.
Find the vertical height h.
[The moment of inertia, I, of a sphere is 2/5 mR^2]
where m is the mass and R is the radius of the sphere.
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I used conservation of energy, such that
1/2 I w^2 = mgh
then substituted the moment of inertia in.
1/5 m R^2 w^2 = mgh
m cancels:
1/5 R^2 w^2 = gh
after this I don't know where to go, i have to relate the angular speed, w, to the speed of the rolling sphere, v.
any ideas?
Find the vertical height h.
[The moment of inertia, I, of a sphere is 2/5 mR^2]
where m is the mass and R is the radius of the sphere.
-------------------------------------------------------------------
I used conservation of energy, such that
1/2 I w^2 = mgh
then substituted the moment of inertia in.
1/5 m R^2 w^2 = mgh
m cancels:
1/5 R^2 w^2 = gh
after this I don't know where to go, i have to relate the angular speed, w, to the speed of the rolling sphere, v.
any ideas?
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