An electric fan is turned off, and its angular velocity...

An electric fan is turned off, and its angular velocity decreases uniformly from 500 rev $/$ min to 200 rev $/ \min$ in 4.00 s. (a) Find the angular acceleration in rev/s $^{2}$ and the number of revolutions made by the motor in the 4.00 s interval. (b) How many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in part (a)?

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Key Concepts

Angular Velocity

Angular velocity is a measure of the rate of change of the angular position of a rotating object. It can be expressed in units such as radians per second or revolutions per minute. This concept is fundamental when analyzing how quickly an object rotates and when relating rotational motion to time.

Angular Acceleration

Angular acceleration is the rate at which the angular velocity changes with time. It is central to understanding the dynamics of rotating systems, especially under conditions of uniform (constant) acceleration or deceleration. It allows for the prediction of how long it takes for an object to change its rotational speed.

Rotational Kinematics

Rotational kinematics involves the equations that describe the motion of rotating bodies under constant angular acceleration. These equations relate angular displacement, initial and final angular velocities, angular acceleration, and time, and are analogous to the linear kinematic equations used in translational motion.

Unit Conversion in Rotational Dynamics

Unit conversion is crucial in rotational dynamics to ensure that all quantities are expressed in consistent units. Converting between units such as revolutions per minute, revolutions per second, and radians per second is important for accurate calculations using the rotational kinematics equations.

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