A rigid object is rotating in a counterclockwise sense around a fixed axis. Each

Question

A rigid object is rotating in a counterclockwise sense around a fixed axis. Each of the following pairs of quantities represents an initial angular position and a final angular position of the rigid object.
(a) Which of the sets can only occur if the rigid object rotates through more than 180°?

3 rad, 6 rad

-1 rad, 1 rad

    1 rad, 5 rad

(b) Suppose the change in angular position for each of these pairs of values occurs in 1 s. Which value represents the lowest average angular speed?

-1 rad, 1 rad

3 rad, 6 rad    

1 rad, 5 rad

Explanation / Answer

( a)

For one rotation , greaterthan 180°, the angular displacement must be larger than radian = 3.14 rad.

Angular displacements for given options

(1) 6 rad – 3 rad = 3 rad

(2) 1 rad – (-1) rad = 2 rad

(3) 5 rad – 1 rad = 4 rad

Only the last option > 3.14 rad.

Thus, the correct option is 1 rad, 5 rad

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(b)

As given angular displacements takes place in the same interval of time, the displacement with the lowest value will be connect with the lowest average angular speed.

Thus, the correct option is -1 rad, 1 rad

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