Question

A disk of mass M and radius R is on the horizontal table, and an external force F is applied to the disk as shown in Figure above. The coefficient of friction between the disk and the table is and it is large enough that the disk is rolling without slipping. The initial velocity of the center of mass is V_3 = 0, the initial angular velocity is 0. Find the acceleration of the center of mass of the disk and the angular acceleration of the disk. Find the velocity of the center of mass of the disk and the angular velocity of the disk as functions of time.

Answer 1

a_0 & V_0 are acceleration and velocity of c,. Wheel rolls without slipping only when velocity of point P is equal to zero V_0 = wR also a_0 = alpha R sigma f_x = M a_0 f_0 - f_s = M a_0 (1) sigma f_Y = 0 Mg = N -(2) sigma tau = I alpha f_s times R = 1/2 MR^2 times alpha alpha = a_0/R f_s times R = 1/2 MR^2 a_0/R f_s = 1/2 M a_0 -(3) 3 eq^n we get f_0 - f_s = Ma_0 Mg = N & f_s = 1/2 Ma_0 f_0 - 1/2 Ma_0 = Ma_0 f_0 = 3/2 Ma_0 a_0 = 2/3 f_0/M alpha = a_0/R = 2/3 f_0/MR solution for part A considering initial velocity angular velocity = 0 { v_i = w_i = 0} so0 using eq^n v = u + at w_f = w_i + alpha t w_f = (2/3 f_0/MR)T using V_0 = wr V_0 = 2/3 f_0/M T solution for