Question

Problem 11.14 Part A A woman of mass m stands at the edge of a solid cylindrical platform of mass M and radius R. At t = 0, the platform is rotating with negligible friction at angular velocity wo about a vertical axis through its center, and the woman begins walking with speed v (relative to the platform) toward the center of the platform. Determine the angular velocity of the system as a function of time. Express your answer in terms of the variables m, M, R, v, wo, and t. 四 ? Submit My Answers Give Up Part B What will be the angular velocity when the woman reaches the center? Express your answer in terms of the variables m, M, and wo w center Submit My Answers Give Up

Answer 1

location of women after time t,

r = R - v t

Applying angular momentum conservation,

Li = Lf

(M R^2/2 + m R^2) w0 = (M R^2/2 + m r^2) w

(M R^2/2 + m R^2) w0 = ( M R^2 / 2 + m (R - vt)^2) w

w = (M R^2 + 2m R^2) w0 / ( M R^2 + 2 m (R - vt)^2)

(B) now r = 0

so ( M R^2 /2 + m R^2) w0 = M R^2 /2 w

w = (M + 2m ) w0 / M