# Angular Speed

"A 243 N sphere 0.199 m in radius rolls, without slipping, 6.06 m down a ramp that is inclined at 36.9Â° with the horizontal. What is the angular speed of the sphere at the bottom of the hill if it starts from rest?"

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#### Solution Preview

at rest, F = mg = 243 N

you know g, find m

at angle 36.9 deg,

243 Cos (theta) = m * a

i.e it just starts to roll

you can find a.

Now find the velocity by the formula,

V^2 - U^2 = 2 ...

#### Solution Summary

"A 243 N sphere 0.199 m in radius rolls, without slipping, 6.06 m down a ramp that is inclined at 36.9Â° with the horizontal. What is the angular speed of the sphere at the bottom of the hill if it starts from rest?"

$2.19