Angular acceleration

Question

A 1 kg mass and a 5 kg mass are attached to either end of a 3 m long massless rod.

If the system is rotated about the center of mass by a force of 7 N acting on the 5 kg mass, (perpendicular to the rod), what will the size of the angular acceleration of the system be

Answer 1

F = 7N

m1 = 1kg

m2 = 5kg

let m2 be at the origin so that

x1 = 3

x2 = 0

let the centre of mass be r, then

r = (m1x1 + m2x2)/(m1+m2) = 3/6 = 1/2

so m2 is 1/2m away from the c.m which means m1 is R = 5/2m away

then the moment of inertia is

I = m1R² + m2r² = 25/4 + 5/4 = 15/2 kgm²

so

torque = Fr = Iα

gives the angular acceleration as

α = Fr/I = 7(1/2)/(15/2) = 7/15 ≈ 0.47rad/s²

.,.,.,.