HonorStudent
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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 :

CastleRook
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: B) [tex]4\pi \text{ radians per sec }[/tex]

Step-by-step explanation:

[tex]\text{Angular velocity} = \frac{\text{ linear velocity}}{\text{radius}}[/tex]

Since, the wheel  covers a distance of [tex]40\pi[/tex] inches in one second.

Thus, its linear velocity = [tex]40\pi\text{ per second}[/tex]

Also, the radius of wheel = 10 inches,

Hence its angular velocity = [tex]\frac{40\pi}{10} = 4\pi\text{ radians per sec}[/tex]

⇒ Option B is correct.

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