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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 dont 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 dont 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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