A machine wheel spins at a rate of 500 revolutions per minute. If the wheel has a diameter of 80 centimeters, what is the angular speed of the wheel, in radians per second? Round your answer to the nearest hundredth.

rad/sec

Angular speed = w = 52.36 rad/s

Linear_velocity = 20.94 m/s

Step-by-step explanation:

A machine wheel spins at a rate of 500 revolutions per minute.

This represents the angular velocity of the machine.

We need to convert it to the appropiate units. (rad/s)

500 rev/min * (2π rad / rev) = 1000π rad/min

1 minute = 60 seconds

1000π rad/min = 1000π rad / (60 s) = 52.36 rad/s

Angular speed = w = 52.36 rad/s

If you need the linear velocity, it i equal to

Linear_v = w*radius

radius = 0.5 * diameter = 0.5 * (80cm) = 40 cm = 0.4 m

Linear_v = (52.36 rad/s) * (0.4 m) = 20.94 m/s