A torsion pendulum is made from a disk of mass m = 6.8 kg and radius R = 0.77 m.

Question

A torsion pendulum is made from a disk of mass m = 6.8 kg and radius R = 0.77 m. A force of F = 48.2 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? (N.m/rad)

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

3. What is the angular frequency of oscillation of this torsion pendulum? (rad/s)

4. Which of the following would change the period of oscillation of this torsion pendulum: increasing the mass, decreasing the initial angular displacement, replacing the disk with a sphere of equal mass and radius, hanging the pendulum in an elevator accelerating downward?

Explanation / Answer

1)the torsion constant of this pendulum
= 48.2 * 0.77 / (0.5* pi )
= 23.63 Nm/ rad ---answer

2)the minimum torque needed to rotate the pendulum a full revolution from equilibrium
= 23.63 * 2 pi
= 148.46 Nm ---answer

3) moment of inertia
= 6.8 * 0.77^2 / 4
= 1.008
Torque = MoI * angular acc
148.46 = 1.008 * a
a= 147.3 rad /s2

s = ut + 0.5 at^2
2 pi = 0 + 0.5 * 147.3 * t^2
t = 0.29 s = period

angular frequency of oscillation of this torsion pendulum
= 1 / t = 3.424 Hz ---answer

4)  hanging the pendulum in an elevator accelerating downward

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