Torque and Rotational Motion

$\frac{1}{2}mL^2$

$\frac{1}{12}mL^2$

$\frac{1}{6}mL^2$

$\frac{1}{3}mL^2$

Off-center collisions perfectly conserve both linear and angular momenta without any translational displacement post-collision.

Centripetal accelerations during impact negligibly affect tangential velocities upon collision alignment.

Sticking together instantaneously means all kinetic energies transform into rotational motion about their common center immediately after impact.

Equal but opposite reaction forces produce internal torques altering individual ball's momenta before completely merging.

The length of the string has no impact on the weight's angular momentum

A longer string causes a decrease in the vertical component of force applied below the pivot point, resulting in lower torque and greater angular momentum

Increasing the length of the string increases the vertical component of the weight's velocity, thus increasing the total angular momentum

An increase in the length of the string results in an increase in the weight's angular momentum

Linear distance

Luminosity

Latent heat

Angular momentum

Watt (W)

Pascal (Pa)

Newton-meter (N·m)

Joule (J)

100J

141 J

45 J

22.5 J

Satellite panel flexibility introduces non-negligible deflection-induced producing unexpected system-wide responses

Uncertainty sheer size large orbiting objects trivially affects overall stability structure

Increased distance main implies gravitational influence drops insignificantly changing dynamic properties

Panels deploy identically regardless environmental conditions such temperature variation exposure solar radiation

Friction doesn't deliver any-angular-impulse as there's no change in external forces.

Friction delivers a negative-angular-impulse, decreasing both rotation rate and clockwise-angular-momentum.

Though motion slows, friction adds equal-and-opposite-angular-impulses so total-angular-momentum stays the same.

Friction creates positive-angular-impulse, increasing its counterclockwise-angular-momentum.

A longer wrench has more mass which inherently increases torque without added force.

A longer wrench reduces friction between the bolt and wrench, requiring less force.

A longer wrench changes the angle at which force is applied, decreasing necessary effort indirectly.

A longer wrench provides greater leverage, increasing torque for the same applied force.

If an external torque acts on a system, the total angular momentum must increase

If no external torques act on a system, the total angular momentum is constant

If no internal forces are present, the total angular momentum must change randomly

If non-external forces act on a system, the total angular momentum must decrease