A pendulum consists of a rod of mass 1 kg and length 1 m connected to a pivot with a solid sphere attached at the other end with mass 0.5 kg and radius 30 cm. What is the torque about the pivot when the pendulum makes an angle of 30° with respect to the vertical?

T = 5.635 Nm

Explanation:

Parameters given:

Mass of rod, m = 1kg

Length of rod, L = 1m

Mass of sphere, M = 0.5kg

Radius of sphere, R = 30 cm = 0.3m

Angle, θ = 30°

Torque is given as:

T = rFsinθ

F represents force. The force acting on both the rod and the sphere is their individual weights. Weight acts at the Centre of a body.

Because the system is made of two parts, the rod and the sphere, we add the individual torque of both parts:

T = mg(L/2)sinθ + Mg(L + R)sinθ

Where g = acceleration due to gravity.

T = ( 1 * 9.8 * 1 * 0.5) sin30 + (0.5 * 9.8 * (1 + 0.3)) sin30

T = (4.9*0.5) + (6.37*0.5)

T = 2.45 + 3.185

T = 5.635 Nm