A torsion pendulum is made from a disk of mass m = 5.2 kg and radius R = 0.65 m.

Question

A torsion pendulum is made from a disk of mass m = 5.2 kg and radius R = 0.65 m. A force of F = 46.6 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

Ineed the steps to the finall answers ...

Explanation / Answer

1)the torsion constant of this pendulum
= 46.6 * 0.65 / (0.5* pi )
= 19.28 Nm/ rad

2)the minimum torque needed to rotate the pendulum a full revolution from equilibrium
= 19.28 * 2 pi
= 121.14 Nm

3) moment of inertia
= 5.2 * 0.65^2 / 4
= .55
Torque = MoI * angular acc
121.14 = .55 * a
a= 220.25 rad /s2

s = ut + 0.5 at^2
2 pi = 0 + 0.5 * 220.25 * t^2
t = 0.24 s = period

angular frequency of oscillation of this torsion pendulum
= 1 / t = 4.166 Hz

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

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