Torque in cylinders - show the cylinder undergoes harmonic motion

In summary, a cylinder suspended by wires undergoes harmonic motion when rotated due to a torque exerted by the wires that is proportional to the rotation angle. The associated period can be computed using the moment of inertia of the cylinder and its angular acceleration.
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Homework Statement



A cylinder of radius R and mass m is suspended using stainless steel
wires attached to fixed supports, so that it can rotate about its axis.
When the cylinder is rotated by an angle a the wires exert a torque
which tends to bring it back to the equilibrium position at a = 0. The
torque exerted by the wires is proportional to a,
 t=-ac
where c > 0 is a constant.

Show that the cylinder undergoes harmonic motion and compute
the associated period.


Homework Equations





The Attempt at a Solution



To be honest I've no idea where to start. I just need a hint to point me in the right direction.

Thanks!
 
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What is the moment of inertial of a solid cylinder, about its axis.

How are torque, moment of inertia, and angular acceleration related?
 

1. What is torque in cylinders?

Torque in cylinders refers to the twisting force that is exerted on a cylinder due to the application of a perpendicular force at a distance from its axis. It is a measure of the cylinder's ability to rotate around its axis.

2. How does torque affect a cylinder's motion?

When a torque is applied to a cylinder, it causes the cylinder to undergo rotational motion. This can be seen in the form of a change in the cylinder's orientation or its angular velocity.

3. What is harmonic motion in cylinders?

Harmonic motion in cylinders refers to a type of motion where the cylinder oscillates or vibrates back and forth in a regular and predictable manner. This is typically seen in systems where a restoring force, such as torque, acts on the cylinder to bring it back to its equilibrium position.

4. How does a cylinder undergo harmonic motion?

A cylinder can undergo harmonic motion when a torque is applied to it, causing it to rotate around its axis. This rotation creates an oscillation or vibration in the cylinder, which can be described as harmonic motion.

5. What factors affect the magnitude of torque in cylinders undergoing harmonic motion?

The magnitude of torque in cylinders undergoing harmonic motion can be affected by several factors, including the distance from the axis of rotation at which the force is applied, the magnitude of the force, and the moment of inertia of the cylinder. Additionally, the frequency and amplitude of the harmonic motion can also impact the torque experienced by the cylinder.

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