A torsion pendulum is made from a disk of mass m = 6.6 kg and radius R = 0.68 m.

Question

A torsion pendulum is made from a disk of mass m = 6.6 kg and radius R = 0.68 m. A force of F = 45.4 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?

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) torsion constant of this pendulum = 45.4 * 0.68 / (0.5* pi ) = 19.65 Nm/ rad

2) minimum torque needed to rotate the pendulum a full revolution from equilibrium = 19.65 * 2 pi = 123.49 Nm

3) moment of inertia = 6.6 * 0.68^2 / 4 = 0.763

Torque = MoI * angular acc

123.49 = 0.763 * a

a = 161.86 rad /s2

s = ut + 0.5 at^2

2 pi = 0 + 0.5 * 161.86 * t^2

t = 0.279 s = period

angular frequency of oscillation of this torsion pendulum = 1 / t = 3.59 Hz

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