Multiple Choice
A fan blade is rotating and speeding up in the counterclockwise direction, which is defined as the positive direction. What are the signs of its angular velocity and angular acceleration ?
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12. Rotational Kinematics
Rotational Velocity & Acceleration
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A wheel of radius 5 m accelerates from 60 RPM to 180 RPM in 2 s. Calculate its angular acceleration.
A
6.28 rad/s2
B
12.6 rad/s2
C
18.8 rad/s2
D
377 rad/s2
Verified step by step guidance1
First, convert the initial angular velocity from revolutions per minute (RPM) to radians per second (rad/s). Use the conversion factor: 1 RPM = \( \frac{2\pi}{60} \) rad/s.
Next, convert the final angular velocity from RPM to rad/s using the same conversion factor.
Determine the change in angular velocity (\( \Delta \omega \)) by subtracting the initial angular velocity from the final angular velocity.
Use the formula for angular acceleration (\( \alpha \)), which is the change in angular velocity divided by the time taken for the change: \( \alpha = \frac{\Delta \omega}{\Delta t} \).
Substitute the values of \( \Delta \omega \) and \( \Delta t \) (2 seconds) into the formula to calculate the angular acceleration.
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