Angular Momentum and Angular Impulse - AP Physics 1

1. What happens to $L$ when radius doubles but mass and velocity remain constant?

   $L$ doubles. Angular momentum is proportional to radius.

2. What is the formula for torque in terms of force and lever arm?

   $\tau = rF\sin(\theta)$. Force times perpendicular distance from axis.

3. Identify the relationship between torque and angular impulse.

   Angular impulse = Torque × Time. Angular impulse is the product of torque and time.

4. What is the formula for angular velocity $\omega$ in terms of period $T$?

   $\omega = \frac{2\pi}{T}$. Relates angular velocity to rotational period.

5. What is the effect of increasing $r$ on $L$ if $v$ is constant?

   $L$ increases. Angular momentum proportional to radius for fixed velocity.

6. State the moment of inertia for a solid cylinder.

   $I = \frac{1}{2}mr^2$. Standard formula for solid cylinder rotating about its axis.

7. How is angular velocity related to angular momentum?

   Angular momentum = Moment of inertia × Angular velocity. Angular momentum equals moment of inertia times angular velocity.

8. What is the moment of inertia for a thin ring?

   $I = mr^2$. All mass at distance $r$ from rotation axis.

9. What is the unit of angular momentum in SI units?

   kg·m²/s. Combines mass (kg), length squared (m²), and time (s).

10. What is the moment of inertia for a point mass?

    $I = mr^2$. All mass concentrated at distance $r$ from axis.

11. What is the formula for angular momentum of a particle?

    $L = r \times p = r \times mv$. Cross product of position vector and linear momentum.

12. Which equation represents the relationship between torque and angular acceleration?

    $\tau = I\alpha$. Newton's second law for rotational motion.

13. How does angular momentum change with increasing rotational speed?

    Angular momentum increases. Angular momentum is proportional to angular velocity.

14. Calculate $L$ for a $1\,\text{kg}$ mass moving at $2\,\text{m/s}$, $r=1\,\text{m}$.

    $L = 2 \text{kg}\cdot\text{m}^2/\text{s}$. Using $L = mvr$: $1 \times 2 \times 1 = 2$.

15. Which equation represents the angular impulse-momentum theorem?

    $J = \Delta L$. Angular impulse equals change in angular momentum.

16. What is the angular momentum of a solid sphere rotating at angular velocity $\omega$?

    $L = I \omega = \frac{2}{5}mr^2 \omega$. Uses the solid sphere moment of inertia formula.

17. What is the conservation law for angular momentum?

    Total angular momentum is constant if no external torque acts. No net external torque means angular momentum stays constant.

18. What is the effect on $L$ if $\omega$ quadruples and $I$ is constant?

    $L$ quadruples. Angular momentum is proportional to angular velocity.

19. What effect does doubling $m$ have on $L$ if $r$ and $v$ are constant?

    $L$ doubles. Angular momentum is proportional to mass.

20. Calculate $L$ for a $2\,\text{kg}$ mass at $3\,\text{m/s}$, $r=4\,\text{m}$.

    $L = 24 \text{kg}\cdot\text{m}^2/\text{s}$. Using $L = mvr$: $2 \times 3 \times 4 = 24$.

21. Which quantity remains constant in an isolated system with no external torque?

    Angular momentum. Conserved quantity in isolated rotational systems.

22. What is the formula for angular acceleration $\alpha$ in terms of $\omega$ and $t$?

    $\alpha = \frac{\Delta \omega}{\Delta t}$. Rate of change of angular velocity.

23. Calculate the angular impulse given $\tau=5\,\text{Nm}$ and $t=3\,\text{s}$.

    Angular impulse = $15 \text{Nm}\cdot\text{s}$. Simple multiplication: $5 \times 3 = 15$.

24. What is the angular momentum of a rotating rod about its center?

    $L = \frac{1}{12}mL^2 \omega$. Uses rod's moment of inertia about center.

25. What is the symbol for angular momentum?

    $L$. Standard symbol for angular momentum in physics.

26. What is the primary cause of a change in angular momentum?

    External torque. Torque is the rotational analog of force.

27. State the formula for angular impulse.

    $J = \tau \times \text{time}$. Angular impulse equals torque multiplied by time duration.

28. Calculate the torque for $r=2\,\text{m}$, $F=10\,\text{N}$, $\theta=90\deg ree$.

    $\tau = 20 \text{Nm}$. Using $\tau = rF\sin(90°)$: $2 \times 10 \times 1 = 20$.

29. What happens to $L$ if the direction of velocity is reversed?

    $L$ reverses direction. Angular momentum is a vector quantity.

30. Find the change in angular momentum given torque $\tau$ and time $t$.

    $\Delta L = \tau \times t$. Angular impulse-momentum theorem application.

31. What is the effect of external torque on a system's angular momentum?

    It changes the angular momentum. Torque causes angular momentum to change over time.

32. State the formula for the moment of inertia of a solid sphere.

    $I = \frac{2}{5}mr^2$. Standard moment of inertia for solid sphere.

33. What is the angular momentum of a disk rotating at $\omega$ with mass $m$ and radius $r$?

    $L = \frac{1}{2}mr^2 \omega$. Uses disk moment of inertia formula.

34. Define angular momentum for a rotating rigid body.

    $L = I \omega$. Fundamental definition for rigid body rotation.

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