1. A rolling wheel of radius r has translational velocity v as well as angular velocity w. Here you will relate translational velocity to angular velocity. Since the circumference of a circle of radius r is 2p r, every time the center of mass moves a distance 2p r, the object rotates a full circle (2p radians). If this happens in a time T then

v = Dx/Dt = 2p r / T (1)

and w = Dq/Dt = 2p/T (2)

Combine these equations to find an expression for w in terms of v.

v = Dx/Dt = 2p r / T (1)

and w = Dq/Dt = 2p/T (2)

Combine these equations to find an expression for w in terms of v.

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