Calculate Moment of Inertia for Clock Pendulum

[moo5003]

Question:

A clock pendulum is an assembly of a very thing 700g rigid rod and a cylinder. The cylinder is 20cm in diameter and has a mass of 3kg. The rod is 70cm long.

A) Find the moment of inertia for the pendulum about the axis passing through the top end of the rod perpendicurlarly to the facet of the cylinder;
b) Calculate the radius of gyration for the pendulum.

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Picture presented above.

A) I = Irod + Icylinder

Irod = (mL^2)/3 + ?

I'm not sure how to get the second one, infact I was confused how they got (ml^2)/3... I can only get (mL^2)/4 when I take the center of mass and treat it as a particle. CM: l/2 to mR^2 to m(l/2)^2 to (mL^2)/4

ANY HELP IS GREATLY APPRECIATED.

 

[marlon]

So are you asking for the moment of inertia of a cylinder ?

Check THIS

Be sure that you know whether the cylinder is solid or not.

marlon

EDIT : you will also need to apply Steiner's Theorem, so make sure you know about what axis you are rotating. This is also important for getting the right I-value for the rod and the cylinder

 

[Doc Al]

You can't find the moment of inertia of an extended body by treating it as if its mass were at its CM! What's the moment of inertia of a thin rod about one end? (Look it up or derive the formula.)

The total moment of inertia is the sum of I(rod) + I(cylinder). When figuring out I(cylinder), be sure to consider that the axis of rotation is not through its center.

 

[mezarashi]

Also if I may add, you may be looking to use the parallel axis theorem after looking up the tables.