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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

Answer :

The angular speed of the wheel, in radians per second is equal to 52.37 rad/sec.

What is an angular speed?

In Mathematics, an angular speed can be defined as the rate of change of angular displacement of a physical object with respect to time. This ultimately implies that, angular speed is a measure of how fast and quickly a physical object revolves or rotates relative to another point or how its angular position changes with respect to time.

Mathematically, the angular speed of a physical object can be calculated by using this formula:

ω = 2πF or ω = Δθ/Δt

Where:

  • ω represents the angular speed.
  • F is the frequency.
  • π is equal to 3.142
  • Δt is the change in time.

Substituting the given parameters into the angular speed formula, we have;

Angular speed of the wheel, ω = 2 × 3.142 × 500

Angular speed of the wheel, ω = 3142 rad/min

In rad/sec, we would divide by 60;

Angular speed of the wheel, ω = 3142/60

Angular speed of the wheel, ω = 52.37 rad/sec.

Read more on angular speed here: https://brainly.com/question/20821713

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