Question

1a.

In the figure here, three particles of mass m = 0.013 kg are fastened to three rods of length d = 0.13 m and negligible mass. The rigid assembly rotates about point o at angular speed w = 0.600 rad/s. About O, what are (a) the rotational inertia of the assembly, (b) the magnitude of the angular momentum of the middle particle, and (c) the magnitude of the angular momentum of the assembly?

1b. A disk with a rotational inertia of 1.20 kg·m² rotates like a merry-go-round while undergoing a torque given by τ = (4.01 + 2.79t) N · m. At time t = 1.00 s, its angular momentum is 3.53 kg·m²/s. What is its angular momentum at t = 3.00 s?

Answer 1

Ans:- (a) m= 0.013 kg ds 0.13 m. w = 0.6 Rad /s m m since rods are mass less moment of inertia of left particle is. Hence ofd *d-*-d 2 md? I, moment of inertia of middle particle is - Iz = m (2 d)² = 4 m d 2 moment of inertia of right most particle is. Is = m (34)² = 9 md2 Hence total moment of inertia of the system about point o is I= I, + I2 + Iz = md² d² + 4md2 tonde I= 14 m 2 = 14 X 0.013 0.0169 I = 3.076 X 16-3 kg ma (b) Angular momentum of middle particle is. ₂ Iz w= 4 m² w 0.0 169 x 0.6 L₂= 4 x 0.013 x -Y L. 5.273 x lo JS Total angular momentum of the system, L= I w= 3.076 x 16 3 X 0.6 -3 L = 1.84 56 x 10 JS