The angular speed of a motor wheel is increased from 1200...

The angular speed of a motor wheel is increased from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration of the motor wheel is (a) $2 \pi \mathrm{rad} \mathrm{s}^{-2}$ (b) $4 \pi \mathrm{rad} 5^{-2}$ (c) $6 \pi \mathrm{rad} \mathrm{s}^{-2}$ (d) $8 \pi \operatorname{rad} s^{-2}$

The angular speed of a motor wheel is increased from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration of the motor wheel is
(a) $2 \pi \mathrm{rad} \mathrm{s}^{-2}$
(b) $4 \pi \mathrm{rad} 5^{-2}$
(c) $6 \pi \mathrm{rad} \mathrm{s}^{-2}$
(d) $8 \pi \operatorname{rad} s^{-2}$

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Key Concepts

Rotational Kinematics

Rotational kinematics is the study of the motion of objects revolving about an axis, focusing on quantities such as angular displacement, angular velocity, and angular acceleration. It involves equations that are analogous to linear kinematics, enabling the analysis of rotational motion under constant or variable acceleration.

Angular Velocity

Angular velocity quantifies how fast an object rotates and is typically measured in radians per second. It indicates the rate of change of the angular position of a rotating body and is often derived from measurements given in revolutions per minute (rpm) by using the conversion factor of 2? radians per revolution.

Angular Acceleration

Angular acceleration represents the rate at which the angular velocity of an object changes over time, measured in radians per second squared. It is calculated by taking the difference between the final and initial angular velocities and dividing by the time interval during which this change occurs.

Unit Conversion (rpm to rad/s)

Converting rotational speed from revolutions per minute (rpm) to radians per second is essential in solving many rotational motion problems. The conversion involves multiplying the rpm value by 2?/60, since one revolution corresponds to 2? radians and one minute contains 60 seconds.

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