Rotational Motion and Equilibrium Practice Flashcards

A set of vocabulary flashcards covering key concepts of rotational motion, torque, moment of inertia, and static equilibrium based on physics exam problems.

Torque ($\tau$)

The product of the force and the lever arm, calculated as $\tau = F \times r \times \sin(\theta)$, measured in units of $N \cdot m$.

Lever arm

The perpendicular distance from the axis of rotation to the line of action of the force, given by the expression $r \sin(\theta)$.

Angular displacement ($\theta$)

The change in the angle as an object rotates, often measured in radians ($rad$). One complete revolution is equal to $2\pi\,rad$.

Angular velocity ($\omega$)

The rate of change of angular displacement over time, often expressed in $rad/s$ or $rad/min$. For example, one counterclockwise rotation in 1 minute equals a velocity of $6.28\,rad/min$.

Angular acceleration ($\alpha$)

The rate of change of angular velocity over time. It is positive for counterclockwise acceleration and negative for deceleration in the counterclockwise direction.

Linear acceleration ($a$)

The rate of change of linear velocity, linked to angular acceleration by the formula $a = r\alpha$, where $r$ is the radius of the rotating object.

Rotational equilibrium

A state in which the sum of the torques acting on an object is zero ($\sum \tau = 0$), meaning clockwise torques are balanced by counterclockwise torques.

Moment of inertia ($I$)

A measure of an object's resistance to change in its rotation, which depends on the object's mass and how that mass is distributed relative to the axis of rotation.

Moment of inertia: Thin hoop

The rotational inertia for an object with all its mass concentrated at the rim, calculated as $I = mr^2$.

Moment of inertia: Solid, uniform cylinder

The rotational inertia for a solid cylinder rotating about its central axis, calculated as $I = \frac{1}{2}mr^2$.

Moment of inertia: Solid, uniform sphere

The rotational inertia for a solid sphere rotating about its center, calculated as $I = \frac{2}{5}mr^2$.

Moment of inertia: Hollow sphere (Thin shell)

The rotational inertia for a sphere with all mass distributed at its surface, calculated as $I = \frac{2}{3}mr^2$. This value is greater than that of a solid sphere of equal mass and radius.

Newton's second law for rotational motion

The relationship stating that torque is equal to the moment of inertia multiplied by the angular acceleration, expressed as $\tau = I\alpha$.

Center of mass

The point on an object through which the force of gravity (weight) is considered to act, used as a reference point for calculating torques and balancing supports.

Static equilibrium

A state where an object remains at rest because both the net force and the net torque acting on it are zero.

Angular frequency

The number of revolutions per unit of time, which can be converted to angular velocity by multiplying by $2\pi$.