Torque, Moment of Inertia, and Rotational Kinematics

Vocabulary flashcards covering key terms and concepts on torque, moment of inertia, static equilibrium, rotational kinematics, rotational inertia, and angular momentum.

Torque

The measure of the turning effect of a rigid body, operationally defined as the product of a perpendicular force and the length of its lever arm from the pivot or axis of rotation.

Lever Arm

A measure of the distance between the force applied to the pivot.

Negative Torque

The direction of torque generated when the rotation is caused by a clockwise force.

Positive Torque

The direction of torque generated when the rotation is caused by a counterclockwise force.

Moment of Inertia

The amount that resists changes in an object's rotating state of motion.

First Condition of Equilibrium

The condition requiring that the sum of all concurrent forces acting on a body is zero ($\Sigma F = 0$).

Second Condition of Equilibrium

The condition requiring that the sum of all torques in a body is zero ($\Sigma \tau = 0$) for the object to be in complete equilibrium.

Rotational Motion

The motion of a body about an internal axis, where the axis of motion is inside the moving object.

Circular Motion

Motion where the axis of the motion is outside the object, which is called an orbit.

Angular Velocity

The time rate of angular displacement for steady rotating motion, expressed as $\omega = \frac{\Delta \theta}{\Delta t}$.

Angular Displacement

The angle around the axis of rotation through which the object rotates, measured in radians.

Radian

The angle subtended at the center of the circle by the arc whose length equals the radius of the circle ($1\text{ radian} = 57.3^\circ$).

Angular Acceleration

The uniform rate of change in angular velocity, denoted by $\alpha = \frac{\Delta \omega}{\Delta t}$.

Rotational Inertia

The resistance of a rotating object to changes in its angular velocity, considering both the shape and mass of the rotating item.

Angular Momentum

The rotational counterpart of momentum denoted by $L$, which for a rotating rigid body is defined as $L = I\omega$ or $L = r \cdot p$.

Law of Conservation of Angular Momentum

Asserts that if there is no net external torque operating on a rigid body, the total angular momentum of the system is conserved ($I_o\omega_o = I_f\omega_f$).