A torsion pendulum is made from a disk of mass m = 7.1 kg and radius R = 0.71 m.

Question

A torsion pendulum is made from a disk of mass m = 7.1 kg and radius R = 0.71 m. A force of F = 42.3 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
= 42.3 * 0.71 / (0.5* pi )
= 19.11 Nm/ rad ---answer

2)the minimum torque needed to rotate the pendulum a full revolution from equilibrium
= 19.11 * 2 pi
= 120.132 Nm ---answer

3) moment of inertia
= 7.1 * 0.71^2 / 4
= 0.8941.025
Torque = MoI * angular acc
120.132 = 0.894 * a
a= 134.25 rad /s2

s = ut + 0.5 at^2
2 pi = 0 + 0.5 * 134 * t^2
t = 0.306 s = period

angular frequency of oscillation of this torsion pendulum
= 1 / t = 3.265 Hz ---answer

4. Increasing the mass & Replacing the disk with a sphere of equal mass and radius

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