The brass pendulum of an heirloom clock consists of 4.6 inch diameter hollow bra

Question

The brass pendulum of an heirloom clock consists of 4.6 inch diameter hollow brass sphere with a weight of 1.8 pounds attached to the end of a 4.2 ft long brass rod with a weight of 3.3 pounds. The pendulum starts from rest at the angle 43

The brass pendulum of an heirloom clock consists of 4.6 inch diameter hollow brass sphere with a weight of 1.8 pounds attached to the end of a 4.2 ft long brass rod with a weight of 3.3 pounds. The pendulum starts from rest at the angle 43 degree. Determine the following quantities. Mass moment of inertia about the pivot point. (include units with answer)

Explanation / Answer

Here ,

the moment of inertia of rod about pivot ,

Irod = ml^2/3

Irod = 3.3 * 4.2^2/3

Irod = 19.4 lb.t^2

now, moment of inertia of sphere about the centre = 0.4 * 1.8 * (4.6/12)^2

Icom = 0.106 lb.ft^2

Now, Using parallel axis theorum ,

moment of inertia of sphere about the pivot

I = Icom = m*d^2

I = 0.106 + 1.8 *(4.2 + 4.6/12)^2

I = 37.92 lb.ft^2

Now, moment of inertia about the pivot of pendulum

Ip = 37.92 + 19.4

Ip = 57.3 lb.ft^2

the moment of inertia about the pivot point is 57.3 lb.ft^2

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