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11 grade physics others

A rotating wheel changes its angular speed from 1800 rpm to 3000 rpm in 20 s. What is the angular acceleration assuming it to be uniform?

  • A. 60π rad-2
  • B. 90π rad-2
  • C. 2π rad-2
  • D. 40π rad-2

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11 Months agoGrade
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1 Answer

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ApprovedApproved Tutor Answer11 Months ago

To find the angular acceleration of a rotating wheel, we can use the formula:

Angular Acceleration Formula

The formula for angular acceleration (α) is:

α = (ω_f - ω_i) / t

where:

  • ω_f = final angular velocity
  • ω_i = initial angular velocity
  • t = time in seconds

Convert RPM to Radians per Second

First, we need to convert the angular speeds from revolutions per minute (rpm) to radians per second (rad/s):

  • ω_i = 1800 rpm = 1800 × (2π rad / 1 rev) × (1 min / 60 s) = 60π rad/s
  • ω_f = 3000 rpm = 3000 × (2π rad / 1 rev) × (1 min / 60 s) = 100π rad/s

Calculate Angular Acceleration

Now, substituting the values into the angular acceleration formula:

α = (100π rad/s - 60π rad/s) / 20 s

α = (40π rad/s) / 20 s = 2π rad/s²

Final Answer

The angular acceleration is 2π rad/s², which corresponds to option C.

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