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 4m, is attached to one end of a string of length /4, 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.

Part A

-How does the magnitude of the angular momentum of puck A about its pivot compare with that of puck B about its pivot?

Part B

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

Explanation / Answer

A) moment of inertia of puck A about first pivot I = m L^2

angular speed w = v/ L
angular momentum = Iw = (m L^2) (v/L) = mvL ......Ans

moment of inertia of puck A about second pivot I = 4m (L/4)^2   = m L^2 / 4

angular speed w = v/ (L /4) = 4v /L

angular momentum = Iw = (m L^2 /4) (4v/L) = mvL    ......Ans

momentum of A / momentum of B = 1

B)

moment of inertia of puck A about first pivot I = m L^2

angular speed w = v/ L
angular momentum = Iw^2 /2   = (m L^2) (v/L)^2 /2   = mv^2 /2 ......Ans

moment of inertia of puck A about second pivot I = 4m (L/4)^2   = m L^2 / 4

angular speed w = v/ (L /4) = 4v /L

angular momentum = Iw = (m L^2 /4) (4v/L)^2   = 2mv^2     ......Ans

KE of A / KE of B = 1/4

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