Question

A ship's propeller of diameter 3 m makes 10.6 revolutions in 30

s. What is the angular velocity of the propeller?
a 90.0 rad/s
b 31.8 rad/s
c 2.22 rad/s
d 66.7 rad/s

Answer 1

Approximately
`2.22\; {\rm rad\cdot s^(-1)}`.

Step-by-step explanation:

Each revolution increases the angular displacement of the propeller by
`2\,\pi` radians. Therefore, after
`10.6` revolutions, the angular displacement of the propeller will be
`(10.6)\, (2\, \pi) = 21.2\,\pi` radians.

Divide angular displacement by the duration to find the angular velocity of this propeller:

`\begin{aligned}\frac{21.2\, \pi\; {\rm rad}}{30\; {\rm s}} \approx 2.22\; {\rm rad\cdot s^(-1)} \end{aligned}`.