Question

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A baseball is thrown with one quarter rotation that takes 1.35 seconds. What is the angular velocity in units of radians per second?

Answer 1

`1.16\:\mathrm{rad/s}`

Explanation:

Angular speed is given by
`\omega=(\Delta \theta)/(\Delta t)`, where
`\Delta \theta` is angle change in radians and
`\Delta t` is elapsed time.

Since the baseball makes one fourth (one quarter) of a rotation in 1.35 seconds, it will take the baseball
`4\cdot 1.35=5.4` seconds to complete on rotation.

One rotation is 360 degrees or
`2\pi` radians. Therefore, the angular speed of the baseball is:

`\omega =(2\pi)/(5.4)=1.16355283466\approx \boxed{1.16\:\mathrm{rad/s}}`