Puck A, of inertia m, is attached to one end of a string of length , and the oth

Question

Puck A, of inertia m, is attached to one end of a string of length , and the other end of the string is attached to a pivot so that the puck is free to revolve on a smooth horizontal surface. Puck B, of inertia 8m, is attached to one end of a string of length /2, and the other end of the string is attached to a second pivot so that B is also free to revolve. In each case, the puck is held as far as possible from the pivot so that the string is taut and then given an initial velocity v perpendicular to the string.

How does the rotational kinetic energy of A compare with that of B?

Explanation / Answer

Moment of inertia of puck A is IA = m

Moment of inertia of puck B is IB = 8m

v =rw

angular velocity of puck A is wA = v/

angular velocity of puck B is wB = 2v/

Rotational kinetic energy of puck A is KA = (1/2)IAwA^2

KA = (1/2)m(v/)2

Rotational kinetic energy of puck B is KB = (1/2)IBwB^2

KB = (1/2)8m(2v/)2

KA/KB = [(1/2)m(v/)2]/[(1/2)8m(2v/)2]

KA/KB = 1/32

KA = KB/32

Rotational energy of Puck A is 1/32 times of Puck B

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