Question

A 310-N sphere 0.20 m in radius rolls without slipping 6.0 m down a ramp that is inclined at 31° with the horizontal. What is the angular speed of the sphere at the bottom of the slope if it starts from rest? X rad/s

Answer 1

Use energy conservation principle to find the required angular speed at the bottom of the slope for the sphere as shown below

for a solid sphere with linear speed u, which is rolling KE - KEfrans + Kenot = // mn2 + 2 / I w² = {mve + Ela mod)) ? 1. = £ mu2 + 1/ s mu? = 70 mu? from energy conservation 1 Ei = Ef 3 mgh = KEF > mgdsino = 2 mu? so 10 => (9.8 m/s2)6m) Sin 31° - 712 5 VE 658 m/s So, w = 72 = m = 32. 9 radls

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