A ball of sticky clay with mass m and velocity v. is shot at a solid cylinder of

Question

A ball of sticky clay with mass m and velocity v. is shot at a solid cylinder of mass Mc and radius R. The cylinder is initially at rest and is mounted to a fixed horizontal axle that runs through its center of mass. The ball is a distance d < R from a line that runs through the center of the cylinder and is perpendicular to the axle. Show that the angular speed of the system just after the clay strikes and sticks to the surface of the cylinder is omega = 2mvid/(Mc + 2m) R2. Is mechanical energy of the clay-cylinder system conserved in this process? Explain your answer. Is momentum of the clay-cylinder system conserved in this process? Explain your answer.

Explanation / Answer

a) conservation of angular momentum

m v d = ( Idisk + m R^2) w

m v d = (1/2 M R^2 + m R^2) w

w = m v d/(1/2 M R^2 + m R^2)

multiply top and bottom by 2

w = 2 m v d/( M + 2 m) R^2

b) since its inelastic collision (things stick)

energy is not conserved

c) there is an external force, that of the the axle so momentum is not conserved

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