Rank the angular speed of the following objects, from highest to lowest: - A bow

Question

Rank the angular speed of the following objects, from highest to lowest: - A bowling ball of radius 12.2 cm rotating at 8.76 radians per second. - A tire of radius 0.541 m rotating at 86.3 rpm. - A 5.84 cm diameter top spinning at 245 degrees per second. - A square, with sides 0.875 m long, whose corners are moving with tangential speed 3.48 m/s as it rotates about its center. - A rock on a string, being swung in a circle of radius 0.167 m with a centripetal acceleration of 9.76 m/s2..

1tire 2rock 3 bowling ball4 top 5 square !!! I tried like this doesnt works..

from the higest angular speed to the lwoest angular speed....

Explanation / Answer

Well the angular speed does not depend on the shape and size of the object. If you are talking of angular momentum or rotational kinetic energy, there will be a difference due to different moment of inertia.

A ball is a hollow sphere. The M.I. will be (2/5)MR2 = 5.95*10-3 M m2

Similarly M.I. of tire will be MR2/2, top will be MR2/2, square will be (4/3)MR2, rock will be (2/5)MR2.

This will give the values of inertia and then you can calculate the angular momentum as : Iwr and Rotational Kinetic Energy as (1/2) Iw2.

w is the angular velocity given.

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