Calculating Moment of Inertia for a Rotating Cylinder | Physics Tutorial

In summary, the conversation discusses finding the moment of inertia for a cylinder with a radius of 20cm and a 50g mass hanging from a light chord wound around it. The formula for energy conservation is used to determine the moment of inertia, with the final speed being higher than the average speed due to starting from rest. The conversation concludes with the agreement that the solution is on the right track.
  • #1
dross
New user has been reminded to post using the Homework Help Template in future schoolwork threads.
Hi I am struggling with the following question.

A cylinder of radius 20cm is mounted on a horizontal axle coincident with its axis and is free to rotate. A light chord is wound onto it and a 50g mass hung from it. After release the mass drops 1m in 12seconds. What is the moment of inertia?

With energy conversation I know the gravitational potential energy lost must equal that of the kinetic energy gained my the mass + the rotational energy gained by the cylinder

0.5mv^2+0.5Iω^2 = mgh

I can rearrange this to find moment of Inertia, I. However is ω = v/r ? with v being 1/12 m/s ?
 
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  • #2
v is not 1/12 m/s. The average speed is 1/12 m/s, but since it starts from rest, the final speed must be higher.
Otherwise you seem on the right track.
 
  • #3
Yep got it. Thanks for your help!
 

What is moment of inertia?

Moment of inertia is a physical quantity that measures an object's resistance to rotational motion. It is also known as rotational inertia.

How is moment of inertia calculated for a rotating cylinder?

The moment of inertia for a rotating cylinder can be calculated using the formula I = ½mr², where m is the mass of the cylinder and r is the radius of the cylinder.

What is the unit of measurement for moment of inertia?

The unit of measurement for moment of inertia is kilogram-meter squared (kg•m²) in the SI system. In the imperial system, it is commonly measured in slug-foot squared (slug•ft²).

What factors affect the moment of inertia of a rotating cylinder?

The moment of inertia of a rotating cylinder is affected by its mass, radius, and distribution of mass. A larger mass or radius will increase the moment of inertia, while a more spread out distribution of mass will decrease it.

Can the moment of inertia of a rotating cylinder be changed?

Yes, the moment of inertia of a rotating cylinder can be changed by altering its mass, radius, or distribution of mass. For example, the moment of inertia can be decreased by removing mass or increasing the radius, and it can be increased by adding mass or decreasing the radius.

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