Question

Determine how long it will take an object to rotate through 20.0 revolutions at an angular velocity of 2.8 radians per second. Use π=3.14. Round the answer to the nearest tenth.

Answer 1

The conversion factor between radians and revolution as measures of angle is 2π rad is equal to 1 revolution. Converting the given angular velocity to rev/s,
                (2.8 rad) x (1 rev / 6.28 rad) = 70/157 revolution per second
Dividing the given angle, 20 rev by the velocity,
                                 (20 rev) / (70/157 rev/s) = 44 6/7 s
Thus, the answer is approximately 44.9 seconds.