The rotor of an electric motor has an angular velocity of 3600 rpm when the load and power are c

step 1 Hi everyone, it is given that rotor of an electric motor has angular velocity 3 ,600 RPM. When t

The rotor of an electric motor has an angular velocity of...

The rotor of an electric motor has an angular velocity of $3600 \mathrm{rpm}$ when the load and power are cut off. The $120-1 b$ rotor, which has a centroidal radius of gyration of $9 \mathrm{in}$, then coasts to rest. Knowing that kinetic friction results in a couple of magnitude 2.5 lb. ft exerted on the rotor, determine the number of revolutions that the rotor executes before coming to rest.

Key Concepts

Friction Torque

Friction torque is the force that opposes rotation, acting as a constant decelerating torque in many situations. It plays a key role in dissipating energy from a rotating system, and understanding its effects allows one to calculate the angular deceleration and total angular displacement (or number of revolutions) before the object stops.

Work-Energy Principle in Rotational Dynamics

The work-energy principle states that the work done by all torques acting on a rotating body is equal to the change in its rotational kinetic energy. In problems where friction (a non-conservative force) does work, this principle helps in determining how far a rotating object will travel before coming to rest by equating the work done by the friction torque to the loss in kinetic energy.

Moment of Inertia

The moment of inertia quantifies the resistance of a rotating body to changes in its angular velocity. It depends on how the mass is distributed relative to the axis of rotation. The concept is central in rotational dynamics, and the radius of gyration provides an effective distance for calculating the moment of inertia as a product of mass and the square of this distance.

Angular Velocity Conversion

This concept involves converting angular speed from one set of units (such as revolutions per minute) to another (such as radians per second). The conversion is necessary because many formulas in rotational dynamics, especially those linked to energy and angular acceleration, require angular velocity in SI or radian-based units.

Rotational Kinetic Energy

Rotational kinetic energy is the energy due to the rotation of an object and is given by one-half the product of the moment of inertia and the square of the angular velocity. This concept is crucial for analyzing systems where energy transformations occur, especially when energy is dissipated by friction or other resistive forces.

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