Angular Momentum and Torque-Angular Momentum Relation

Vocabulary flashcards reviewing concepts, formulas, unit measurements, and worked examples from lecture notes on angular momentum and torque.

Linear Momentum

A physical quantity that describes the motion of an object moving in a straight line.

Angular Momentum

A quantity that describes how much rotational motion an object has, measured in units of $kg\,m^2/s$.

Angular Momentum of a Particle ($L$)

The rotational momentum of a particle moving in a circular path, given by the formula $L = m v r$, where $m$ is mass in $kg$, $v$ is tangential velocity in $m/s$, and $r$ is distance from the axis of rotation in $m$.

Angular Momentum of a Rigid Object ($L$)

The rotational momentum of a rigid object, given by the formula $L = I \omega$, where $I$ is moment of inertia in $kg\,m^2$ and $\omega$ is angular velocity in $rad/s$.

Moment of Inertia ($I$)

A property of a rotating object measured in $kg\,m^2$ that represents how difficult the object is to rotate.

Angular Velocity ($\omega$)

A measure of how fast an object rotates around an axis, expressed in $rad/s$.

Torque-Angular Momentum Relation

The formula $\tau = \frac{\Delta L}{\Delta t}$, which states that net torque $\tau$ in $N\,m$ equals the rate of change of angular momentum over time interval $\Delta t$.

Change in Angular Momentum ($\Delta L$)

The product of net torque and the time interval during which it acts, expressed as $\Delta L = \tau \Delta t$ or $\Delta L = L_f - L_i$.

Final Angular Momentum ($L_f$)

The total angular momentum of an object after torque has acted upon it, calculated as $L_f = L_i + \tau \Delta t$.

Constant Angular Momentum Condition

The rule stating that angular momentum remains constant when there is no net external torque acting on the object.

Example 1 (Particle Angular Momentum Calculation)

For a $2\,kg$ object moving at $3\,m/s$ in a circular path with a radius of $4\,m$, angular momentum is calculated as $L = (2)(3)(4) = 24\,kg\,m^2/s$.

Example 2 (Rigid Object Angular Momentum Calculation)

For a wheel with a moment of inertia of $2\,kg\,m^2$ rotating at $5\,rad/s$, angular momentum is calculated as $L = (2)(5) = 10\,kg\,m^2/s$.

Example 3 (Change in Angular Momentum Calculation)

For a torque of $4\,N\,m$ acting on a wheel for $3\,s$, the change in angular momentum is calculated as $\Delta L = (4)(3) = 12\,kg\,m^2/s$.

Example 4 (Final Angular Momentum Calculation)

For a wheel initially at $L_i = 10\,kg\,m^2/s$ acted on by $2\,N\,m$ of torque for $5\,s$, $\Delta L = 10\,kg\,m^2/s$ and $L_f = 10 + 10 = 20\,kg\,m^2/s$.