Question

What is the angular velocity of an object described by the following plot at t=5\sect=5sec (in radians/s)?

Answer 1

5 rad /s

Step-by-step explanation:

The angular velocity is defined by

`\omega=(\Delta\theta)/(\Delta t)`

This means that the angular frequency is the slope of the θ vs. time graph.

Therefore, our original question is rephrased to the following.

What is the slope of the θ vs. time graph at t = 5s?

We find the slope using points (0, 25) and ( 5, 50).

`\omega=(\Delta\theta)/(\Delta t)=(50-25)/(5-0)`

`\Rightarrow(25)/(5)`

`\Rightarrow\boxed{\omega=5.}`

Hence, the angular frequency of the object is 5 radians/sec.