Question

1. determine the angular velocity of a bicycle tire that rotates 60 times per minute?

1.57 \\(\frac{\text{rad}}{\text{s}}\\)
12.57 \\(\frac{\text{rad}}{\text{s}}\\)
6.28 \\(\frac{\text{rad}}{\text{s}}\\)
3.14 \\(\frac{\text{rad}}{\text{s}}\\)

Explanation:

Step1: Find rotations per second

$\frac{60 \text{ rotations}}{1 \text{ minute}} = \frac{60 \text{ rotations}}{60 \text{ seconds}} = 1 \text{ rotation/s}$

Step2: Convert to angular displacement

1 full rotation = $2\pi$ radians, so:
$\text{Angular displacement per second} = 1 \times 2\pi = 2\pi \text{ rad/s}$

Step3: Calculate numerical value

Substitute $\pi \approx 3.14$:
$2\pi \approx 2 \times 3.14 = 6.28 \text{ rad/s}$

Answer:

6.28 $\frac{\text{rad}}{\text{s}}$