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 3.42 radians per second.

- A tire of radius 0.341 m rotating at 35.4 rpm.

- A 5.34 cm diameter top spinning at 145 degrees per second.

- A square, with sides 0.625 m long, whose corners are moving with tangential speed 1.78 m/s as it rotates about its center.

- A rock on a string, being swung in a circle of radius 0.548 m with a centripetal acceleration of 16.5 m/s2

RANK FROM HIGH ANGULAR SPEED TO LOWEST ANGULAR SPEED with the bold words.

thank you

Explanation / Answer

Angular velocity W = 2pi/T or W = V/r

so

for Bowling ball, W = 3.42 rad/s

for tire, W = 35.4 rpm = 35.4 * 2pi/60 = 3.707 rad/s

for TOp, 360 deg = 2pi radians, 145 deg/s = 145* 2pi/360 = 2.53 rad/s

for square , W = v/r = 1.78/0.625 --------> W = 2.848 rad/s

for Rock, accleration a = rW^2 , W^2 = sqrt(a/r) = sqrt(16.5/0.548------->W = 5.48 rad/s

so now the order

ROCK > TIRE > BOWLING BALL > SQUARE > TOP

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