Question

Two disks are fused into one body that is free to rotate about an axis through its center, as shown. The inner disk has a radius a = 20 cm and a 60 N weight is suspended vertically from string wrapped around it. The outer disk has radius b = 40 cm and a force of magnitude F is applied tangent to its rim. What value of F is required to give zero net torque about their common center?

Answer 1

Radius of inner disc, r1 = 20 cm = 0.20 m

Weight suspended vertically from string wrapped around the inner disc, w = 60 N

The torque produced due to the weight, Ꞇ = r1 X w = 0.2 x 60 =12 Nm

The radius of outer disc, r2 = 40 cm = 0.40 m

A force F applied tangential to the outer disc produces a torque Ꞇ1 = r2 x F

To give zero net torque about their common centre, Ꞇ = Ꞇ1

                        12 = r2 x F

                        F = 12/r2 = 12 / 0.4 = 30N

The value of force F = 30 N