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°?A. 3 rad, 6 radB. -1 rad, 1 radC. 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?

A. -1 rad, 1 radB. 3 rad, 6 rad C. 1 rad, 5 rad

Answer 1

Answer: (a) 1 rad, 5 rad

(b) -1 rad, 1 rad

Step-by-step explanation:

180° = Π radians

Since pi has a value greater than 3,

The angular distance between the two points has to be greater than 3 radians

a) Only option C has an angular distance greater than 3rad (5-1= 4rad)

b) angular velocity = w = 2Πf

The lowest angular distance is -1rad, 1rad

1-(-1) rad = 2rad

Since the change in all of their positions happened in 1 second, option A has the lowest angular velocity for rotating the least in the same time.