Question

In the figure below a cylinder having a mass of 3.0 kg can rotate about its central axis through point O. Forces are applied as shown: ₁ = 3.0 N, ₂ = 2.0 N, ₃ = 1.0 N, and ₄ = 2.0 N. Also, r = 5.0 cm and R = 12 cm.

Find the magnitude and direction of the angular acceleration of the cylinder. (During the rotation, the forces maintain their same angles relative to the cylinder.)

magnitude ___ rad/s²

^{direction ( clockwise or counterclockwise)}

Answer 1

According to the sign conventions, the magnitude of the net torque exerted on the cylinder of massm and radius Ris Thet = FR FR - F3 = (3-1) 6-18m)-(N) 6-12 m)-(1)-05m 0:0# Nor) For the cylinder, I = I MR² $(3 Kg) (6.1260) I = 0.0216 kg.me Tnet = Id x= Thet 0.07 Nom 0.0 216 kg.me = 3.24074044) rad/ov x = 13.24 (radys Courtenclockwise