A grinding wheel with a 28cm diameter spins at a rate of 2020 revolutions per minute. What is the linear speed of the rim of the wheel?
(28π cm/rev) * (2020 rev/min) = 56560π cm/min
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To determine the linear speed of the rim of the grinding wheel, you need to use the formula:
Linear Speed = Circumference × Number of revolutions per minute
First, let's calculate the circumference of the grinding wheel. The circumference of a circle can be found using the formula:
Circumference = 2 × π × Radius
Since the diameter of the wheel is given, you need to divide it by 2 to find the radius:
Radius = Diameter / 2
Substituting the values:
Radius = 28 cm / 2 = 14 cm
Next, calculate the circumference:
Circumference = 2 × π × 14 cm
Now, we will convert the revolutions per minute to revolutions per second. Since there are 60 seconds in a minute, you divide the revolutions per minute by 60:
Revolutions per Second = Revolutions per Minute / 60
Substituting the values:
Revolutions per Second = 2020 revolutions per minute / 60 = 33.67 revolutions per second
Finally, substitute the values you calculated into the linear speed formula:
Linear Speed = Circumference × Revolutions per Second
Linear Speed = 2 × π × 14 cm × 33.67 revolutions per second
By multiplying the terms together, you can find the answer to your question.