Angular Momentum and Angular Impulse - AP Physics C Mechanics

1. State the equation relating angular impulse and change in angular momentum.

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

2. What is the effect of applying a net torque on a system?

   It changes the angular momentum. Net torque causes angular momentum to change over time.

3. Determine the change in angular momentum for a 10 Nm torque applied for 5 s.

   $\triangle L = 50 \text{ Nms}$. Apply $\triangle L = \tau \triangle t$: $10 \times 5 = 50$.

4. What is the SI unit of angular momentum?

   Kilogram meter squared per second (kg·m²/s). Derived from $[mass][length]^2[time]^{-1}$.

5. What is the formula for angular impulse?

   $J = \tau \times \triangle t$. Product of average torque and time interval.

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

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

7. Calculate angular momentum for a mass of 2 kg at 4 m/s, radius 1 m.

   $L = 8 \text{ kg}\text{m}^2/\text{s}$. Apply formula: $L = mvr = 2 \times 4 \times 1 = 8$.

8. What is the formula for change in angular momentum?

   $\triangle L = \tau \times \triangle t$. Angular impulse-momentum theorem for rotational motion.

9. What is the angular momentum of a point mass $m$ at distance $r$?

   $L = mvr \times \text{sin}(\theta)$. Includes perpendicular component of velocity to radius vector.

10. Find the angular momentum of a 5 kg mass at 3 m/s, radius 2 m.

    $L = 30 \text{ kg}\text{m}^2/\text{s}$. Calculate: $L = mvr = 5 \times 3 \times 2 = 30$.

11. What is the formula for the moment of inertia of a thin rod about its center?

    $I = \frac{1}{12}ml^2$. Standard moment of inertia for uniform thin rod.

12. Find angular momentum of a 3 kg particle moving at 2 m/s, radius 4 m.

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

13. State the conservation of angular momentum principle.

    Total angular momentum is constant if net external torque is zero. Fundamental principle for rotational systems without external torques.

14. Calculate angular impulse if torque is 5 Nm over 3 s.

    $J = 15 \text{ Nms}$. Angular impulse equals torque times time interval.

15. What is required for a change in angular momentum?

    A net external torque. Only external torques can change system's angular momentum.

16. If net external torque is zero, what happens to angular momentum?

    It remains constant. Conservation of angular momentum applies when $\tau_{ext} = 0$.

17. What is the effect of a constant external torque on a system?

    It results in a constant change in angular momentum. Constant torque produces linear change in angular momentum.

18. What is the moment of inertia for a solid cylinder?

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

19. What happens to angular velocity if moment of inertia increases?

    Angular velocity decreases if angular momentum is constant. From $L = I\omega$, if $I$ increases then $\omega$ decreases.

20. What determines the direction of angular momentum?

    The right-hand rule. Curl fingers with rotation, thumb points in $\vec{L}$ direction.

21. How is angular momentum affected by a perpendicular force?

    It causes a change in angular momentum. Perpendicular force creates torque, changing angular momentum.

22. What is the moment of inertia for a solid sphere?

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

23. Identify the units of torque.

    Newton meter (Nm). Standard SI unit for torque, equivalent to kg⋅m²⋅s⁻².

24. State the principle of angular momentum conservation.

    Angular momentum is conserved in the absence of external torques. Fundamental law for isolated rotational systems.

25. How is angular momentum conserved in an isolated system?

    No external torque implies constant angular momentum. Zero net external torque ensures angular momentum conservation.

26. State the formula for torque in terms of force and lever arm.

    $\tau = r \times F \times \text{sin}(\theta)$. Perpendicular distance from axis multiplied by force component.

27. Identify the symbol for angular momentum.

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

28. What happens to angular momentum if no external torques act?

    It remains constant. Angular momentum conservation when no external torques present.

29. Calculate the angular impulse from a torque of 8 Nm applied for 2 s.

    $J = 16 \text{ Nms}$. Torque-time product: $8 \times 2 = 16$.

30. Calculate the change in angular momentum for $\tau = 6 \text{ Nm}$ over $t = 4 \text{ s}$.

    $\triangle L = 24 \text{ Nms}$. Apply impulse formula: $\triangle L = \tau \triangle t = 6 \times 4 = 24$.

31. Identify the relationship between torque and angular momentum.

    $\tau = \frac{dL}{dt}$. Torque equals the time rate of change of angular momentum.

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