Multiple Choice
Calculate the rotational velocity (in rad/s) of a clock's minute hand.
EXTRA:Calculate the rotational velocity (in rad/s) of a clock's hour hand.
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12. Rotational Kinematics
Rotational Velocity & Acceleration
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A person runs ¼ of the way around a circular lake in 5.6 minutes. What is the person's angular speed?
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Verified step by step guidance1
First, understand that angular speed is defined as the rate at which an object moves through an angle. It is given by the formula: \( \omega = \frac{\Delta \theta}{\Delta t} \), where \( \omega \) is the angular speed, \( \Delta \theta \) is the change in angle, and \( \Delta t \) is the change in time.
Identify the change in angle \( \Delta \theta \). Since the person runs ¼ of the way around a circular lake, the change in angle is \( \frac{1}{4} \times 2\pi \) radians, because a full circle is \( 2\pi \) radians.
Calculate \( \Delta \theta \) using the formula: \( \Delta \theta = \frac{1}{4} \times 2\pi = \frac{\pi}{2} \) radians.
Identify the change in time \( \Delta t \). The problem states that the person runs this distance in 5.6 minutes. Convert this time into seconds: \( 5.6 \times 60 = 336 \) seconds.
Substitute \( \Delta \theta \) and \( \Delta t \) into the angular speed formula: \( \omega = \frac{\frac{\pi}{2}}{336} \). Simplify this expression to find the angular speed in radians per second.
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