A wheel spins through 29 revolutions per minute. Find the angular velocity and the linear velocity if the radius of the wheel is 1.8 feet.

w=? (rad/min)
v=? (feet/min)

Is my answer correct?

w=(29/1)(2pi/1)
w=~182.2124 rad/min

v=(1.8)(182.2124)
v=~327.9823 feet/min

looks good to me.

Hey. How did you find it?

To find the angular velocity, we need to convert the number of revolutions per minute into radians per minute. Recall that 1 revolution equals 2π radians.

Here's how you can calculate the angular velocity (ω):

1. Convert the number of revolutions per minute to radians per minute:
ω = (number of revolutions) * (2π radians / 1 revolution) = 29 * 2π radians / min

Therefore, the angular velocity (ω) is 58π radians per minute.

To find the linear velocity (v), we can use the formula:

v = ω * r,

where r is the radius of the wheel.

Here's how you can calculate the linear velocity (v):

1. Substitute the values into the formula:
v = 58π rad/min * 1.8 ft

2. Simplify:
v ≈ 164.934 ft/min

Therefore, the angular velocity (ω) is approximately 58π radians per minute, and the linear velocity (v) is approximately 164.934 feet per minute.