Question

A torsion pendulum is made from a disk of mass m = 5.7 kg and radius R = 0.67 m. A force of F = 43 N exerted on the edge of the disk rotates the disk 1/4 of a revolution from equilibrium.

1. What is the torsion constant of this pendulum?

2. What is the minimum torque needed to rotate the pendulum a full revolution from equilibrium?

3. What is the angular frequency of oscillation of this torsion pendulum?

Answer 1

1)the torsion constant of this pendulum

= 43 * 0.67 / (0.5* pi )

= 18.34 Nm/ rad ---answer

2)the minimum torque needed to rotate the pendulum a full revolution from equilibrium

= 18.34* 2 pi

= 115.24 Nm ---answer

3) moment of inertia

= 5.7 * 0.67^2 / 4

= 0.64

Torque = MoI * angular acc

115.24 = 0.64 * a

a= 180.06 rad /s2

s = ut + 0.5 at^2

2 pi = 0 + 0.5 * 180.06 * t^2

t = 0.264 s = period

angular frequency of oscillation of this torsion pendulum

= 1 / t = 3.79 Hz ---answer