Question

A wheel with a radius 10 inches covers a distance of 40pie inches in one second. What is the angular speed of this wheel?

A) 2pie radians per/sec
B) 4pie radians per/sec
C) pie radians per/sec
D) 2 radians per/sec
E) 4 radians per/sec
F) None of these

Answer 1

angular velocity is given by:
ω=v/r
where:
ω=angular velocity
v=linear velocity
r=radius
From the question;
v=40π inches/sec
r=10
therefore:
ω=40π/10= 4π radians per per/sec

Answer 2

Answer: B) $4\pi \text{ radians per sec }$

Step-by-step explanation:

$\text{Angular velocity} = \frac{\text{ linear velocity}}{\text{radius}}$

Since, the wheel  covers a distance of $40\pi$ inches in one second.

Thus, its linear velocity = $40\pi\text{ per second}$

Also, the radius of wheel = 10 inches,

Hence its angular velocity = $\frac{40\pi}{10} = 4\pi\text{ radians per sec}$

⇒ Option B is correct.