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A solid spherical ball of mass m and radius R rolls without slipping, down an inclined plane that makes an angle @ with the horizontal. There is a frictional force exerted on the ball by the incline, but it is not necessary to know the coefficient of friction to do the problem. The ball starts from rest. Calculate the velocity Vcm of the center of mass of the ball after it has been rolling for t seconds. (hint. consider, among other things, the torque exerted about an exists of rotation through the center of the spherical ball. note that is is not necessary to know where on the plane the ball begins rolling

2006-12-13 10:49:01 · 2 answers · asked by Mark K W 1 in Science & Mathematics Physics

2 answers

The torque about the ball's center is r*mg*sin@ = T
Angular acceleration α = T/I where I = (2/5)mr² so,

α = (5/2)g*sin@/r and ω = α*t Finally,

v = rω = (5/2)tgsin@

2006-12-13 12:17:00 · answer #1 · answered by Steve 7 · 0 0

(sin(@)) * 9.8= Acceleration (A)

A * t =velocity at given time (V)

the radius of the sphere doesn't matter. Because no matter the size of an object, they all fall at the same rate. The only thing that differentiates velocity is friction (surface area). But, since that's not used in this scenario, the R is not important.

2006-12-13 19:00:35 · answer #2 · answered by jpferrierjr 4 · 0 0

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