You and your friend are going on a bike ride. On a boring, flat section of the r

Question

You and your friend are going on a bike ride. On a boring, flat section of the road you begin chatting about the speeds of points on the bicycle wheel with respect to the road. Your friend asks, “At any instant, how does the linear velocity with respect to the ground of the point at the top of the wheel compare with the linear velocity with respect to the ground of the point at the bottom of the wheel?”

What is your answer? Construct an argument to justify your conclusion. Explain your position clearly and completely by providing all reasons that supports your conclusion.

Explanation / Answer

since we know that the bike wheels re rolling without slipping on the ground and hence the velocity of the center of the wheel is v = r*w

where w = angular velocity of the wheel about it's center.

now since the wheel is rolling without slipping the point at the bottom of the wheel is zero.

now the velocity of the top most point is V = r*w + v = 2v

hence the velocity of the topmost point is 2v while that of the bottom most point is zero, where v is the velocity of the center of the wheel w.r.t the ground

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