If the hour and minute hands on a clock have a common axis of rotation and equal mass and the minute hand is long and thin whilst the hour hand is short and thick, which has a greater moment of inertia?
I thought the hour hand would have the greater moment of inertia because it's heavier, but I'm not really sure. Does anybody else have ideas?
2007-01-25 10:50:56 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Physics
The small longer minute hand. Here is why. It has a rotational velocity 12 times that of the small hand. Remember Inertia=mass x velocity.
So no way is the mass of the small hour hand = to 12 times the mass of the littler minute hand. Just to have same inertia it would have to have that.
Lets not get 'moment of inertia' confused with common inertia. Moment of inertia is a measure of a physical property of a mass and is equal to Sigma of mass x incremental discances to each mass unit. That is basically an integral calculus problem of which I am sure is not what you want.
Answer is the small little hand because of the 12 times higher velocity.
2007-01-25 11:03:56 · answer #1 · answered by James M 6 · 0⤊ 0⤋
The wiki link lists moments of interia for some common shapes and points of rotation. The momentum of inertia for this example (uniform rod of mass m length L, rotating at one end) is:
I = 1/3 m L²
So, for the mass as the hour hand, the minute hand, being longer, would have a greater momentum of inertia.
For a "feel" for why this should be, imagine trying to rotate in your hand a heavy but very short bar of steel, and the same thing if it was stretched as long as a fishing rod.
2007-01-25 11:04:53 · answer #2 · answered by Scythian1950 7 · 0⤊ 0⤋
Hour hand heavier? Did you read your own problem--the part about equal mass.
The minute hand is going to have a greater moment because it carries more mass further away from the axis.
The equation (which you don't need here) is:
Moment of inertia equals the integral of r^2 dm. So if more of the mass (dm) is further out, you'll have a greater moment.
2007-01-25 10:59:18 · answer #3 · answered by Anonymous · 0⤊ 0⤋
I agree with you. I think the mass of the hour hand would increase its inertia. Then are we talking about a vacuum environment or an atmospheric one?
2007-01-25 10:59:49 · answer #4 · answered by woofan60 3 · 0⤊ 1⤋