Question

front view side view FT 1 R Ms Pulling the yo-yo [9pt] A non-intuitive motion that combines translation and rotation is pulling a wheel with a string wrapped around it, as shown in the figure above. Depending on what angle the string is pulled, you can obtain three kinds of motion: the yo-yo accelerating in the direction of the applied tension force and winding up, the yo-yo accelerating in the opposite direction of tension and unwinding, and the yo-yo sliding at constant speed and no change in string length. For this problem, assume our yo-yo consists of two identical solid disks of mass M=0.50 kg and radius R = 30 cm with an effectively massless solid axle of mass 14 -0.15 kg and radius HAR 15 em connecting them. A light string is wrapped around the axle, which is also effectively massless compared to the yo-yo disks. The yo-yo sits on a flat table with maximum static and kinetic coefficients of friction us = ulk = 0.80 acting between the wheel and table surfaces. (a) [2 pt] Compute the moment of inertia of the yo-yo about its center of mass. (b) [4 pt] Assume the yo-yo is pulled directly to the left and rolls without slipping. Using Newton's 2nd Laws for translation and rotation, determine the magnitude of tension force and the translational and angular acceleration vectors (magnitude and direction) assuming that the maximum static friction force acts on the yo-yo. () [3 pt] Now consider that the string is pulled upward at an angle relative to horizontal. At what angle would the system be in equilibrium, so that there is neither translational nor angular acceleration?

Answer 1

Part - (al) The moment inertia of the center of mass vo vo about it's is I MR² 2 K 1 0-5•( 30x1042) . 2 0.25 X 0.09 = o.osas kg-m-1 (6) ) (. R ha for rotation torque t = Patucale eling Ia torque about center of mass we have ㄷ FR 2 where for is frictional force f = 0.80 x mg = 0.8 x 015.X10 N

Sa { =4N. torque :T=R(Ex =) by using t= I'd T= I'd we get angular acceleration 셔 R(F 1 uf - 포 I ㅠ oog5 + 아 > K - 13:33 ( ) [a= 1359(틀) 튕 a = 4444 (4) translational acceleration a= 두 5 M

(C) The string would be in Ft equillibrium when E (9) F Caro & Ę Sing = Mg mg tano = π f tan or 5 T tano = 1.25 4 V tan" (1.25) Am