Question

1. a skateboard wheel rotates at an angular velocity of $75\frac{\text{rad}}{\text{s}}$. how many revolutions does it make in 30 seconds? \bigcirc 179 revolutions \bigcirc 358.1 revolutions \bigcirc 14324 revolutions \bigcirc 716.2 revolutions

Explanation:

Step1: Calculate total angular displacement

$\text{Total angular displacement} = 75\ \frac{\text{rad}}{\text{s}} \times 30\ \text{s} = 2250\ \text{rad}$

Step2: Convert radians to revolutions

Since $1\ \text{revolution} = 2\pi\ \text{rad}$,
$\text{Number of revolutions} = \frac{2250}{2\pi} \approx 358.1$

Answer:

358.1 revolutions