A torsion pendulum is made from a disk of mass m = 6.9 kg and radius R = 0.79 m.

Question

A torsion pendulum is made from a disk of mass m = 6.9 kg and radius R = 0.79 m. A force of F = 48.8 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

Solution-

1)the torsion constant of this pendulum
= 48.8 * 0.79 / (0.5* pi )
= 24.55 Nm/ rad ---answer

2)the minimum torque needed to rotate the pendulum a full revolution from equilibrium
= 24.55 * 2 pi
= 154.17 Nm ---answer

3) moment of inertia
= 6.9 * 0.79^2 / 4
= 1.08
Torque = MoI * angular acc
154.17 = 1.08 * a
a= 142.75 rad /s2

s = ut + 0.5 at^2
2 pi = 0 + 0.5 * 142.75 * t^2
t = 0.297 s = period

angular frequency of oscillation of this torsion pendulum
= 1 / t = 3.37 Hz

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

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