Fly Fishing Guides

Travel Rod

Rotation in Physics. A thin Rod of length.75 m and mas .42 kg is suspended frely from one end.?

It is pulled to one side and then allowed to swing like a pendulum passing through its lowest position with angular speed 4.0 rad/s. neglecting friction and air resistance, find (a) the rod’s KINETIC energy at its lowest position and (b ) hhow far above that position the center of mass rises.

Answer: .63 J

If we calculate the rotational kinetic energy at that point (after finding the inertia of the system), the answer matches the bookl’s — .63 J. However, I tried to find same answer with another approach. In particular, I let thegeometric center of the rod ( assuming its uniform) be the center of mass. I supposed that the center of mass of the rod traveled down a distance of L/2, and tried to find the energy using theconservation of Mechanical energy. However, I think it did not give me the same answer.

Please, tell me why cannot I make such an assumption.

When a rod is rotating about its end, the particles at the end remote from the pivot are moving faster than those close to the pivot. For rotational calculations, you use the moment of inertia of the rod, which takes account of this as it is the sum of mr^2 for each particle in the rod.

By using the centre of mass, you are assuming that all the mass of the rod is concentrated at its centre, and therefore all at the same distance from the pivot. This approach is suitable only for statics and linear motion calculations — not for rotation.

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Hot Rod Travel Trailer

Travel Rod AMAZON PRODUCTS BELOW

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