Conservation of Angular Momentum - AP Physics 1

1. If a figure skater pulls in their arms, what happens to their spin rate?

   Spin rate increases. Arms closer reduces $I$, so $\omega$ increases to conserve $L$.

2. What happens to a figure skater's angular momentum when they pull their arms in?

   Remains constant. Conservation applies - only $I$ and $\omega$ change, not $L$.

3. Define the term 'torque'.

   A measure of the force that can cause an object to rotate about an axis. Rotational analog of force for linear motion.

4. What is the effect of a net external force on a system's angular momentum?

   It can change the system's angular momentum. External forces can create torques that change $L$.

5. What is the formula for angular momentum $L$ of a point mass?

   $L = mvr \sin \theta$. For point mass: momentum times radius times sine of angle.

6. What is the relationship between torque and change in angular momentum?

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

7. What occurs when a rotating object experiences a change in distribution of mass?

   Its moment of inertia changes. Redistributing mass changes the moment of inertia $I$.

8. State the effect of an increase in rotational speed on moment of inertia.

   No effect; moment of inertia is mass and shape dependent. Moment of inertia depends only on mass distribution.

9. Describe the angular momentum of a system with no external torques.

   Remains constant. Conservation principle applies when no external torques present.

10. Calculate angular momentum change if torque is applied for time $t$.

    $\Delta L = \tau t$. Impulse-momentum theorem applied to rotational motion.

11. What is the relationship between angular momentum and linear momentum?

    Angular momentum is the rotational analog of linear momentum. Both describe inertial motion in their respective domains.

12. What does $I$ represent in the angular momentum formula $L = I\omega$?

    Moment of inertia. Rotational inertia - resistance to angular acceleration.

13. For a rotating rod, what is the expression for its moment of inertia about its end?

    $I = \frac{1}{3}mL^2$. Standard formula for rod rotating about one end.

14. What is the angular momentum of an object with zero angular velocity?

    Zero. Since $L = I\omega$, zero angular velocity gives zero $L$.

15. What does $\omega$ represent in the formula $L = I\omega$?

    Angular velocity. Rate of rotation measured in radians per second.

16. How does the conservation of angular momentum apply to a spinning top?

    The top spins with constant angular momentum if no external torque acts. Applies when friction and air resistance are negligible.

17. What is the formula for torque $\tau$?

    $\tau = rF \sin \theta$. Force times lever arm times sine of angle between them.

18. What is the angular momentum of a solid sphere rotating about its center?

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

19. If a spinning disk's moment of inertia increases, what happens to its angular velocity?

    Angular velocity decreases. Since $L = I\omega$, larger $I$ requires smaller $\omega$.

20. Identify the formula for angular momentum of a rotating body.

    $L = I\omega$. For rigid bodies: moment of inertia times angular velocity.

21. What happens to a wheel's angular momentum if its speed triples?

    Angular momentum triples. Angular momentum is directly proportional to angular velocity.

22. How does angular velocity change if the radius is halved while conserving angular momentum?

    Angular velocity quadruples. Since $I = mr^2$, halving $r$ quarters $I$, so $\omega$ quadruples.

23. Identify the variable that represents angular velocity.

    $\omega$. Greek omega represents angular velocity in physics.

24. What is the effect of increasing moment of inertia on a system's stability?

    Stability increases. Larger $I$ resists changes in rotational motion.

25. How does angular momentum apply to planetary orbits?

    Planets conserve angular momentum unless acted upon by external forces. Kepler's laws follow from angular momentum conservation.

26. State the conservation of angular momentum principle.

    Total angular momentum remains constant if no external torque acts. Fundamental principle when no external torques act on system.

27. What is the effect of friction on angular momentum?

    Friction can reduce angular momentum by exerting external torque. Creates external torque that opposes rotational motion.

28. Calculate the angular momentum of a 2 kg mass moving at 4 m/s in a circle of radius 0.5 m.

    $L = 4 \text{ kg} \cdot \text{m}^2/\text{s}$. $L = mvr = 2 \times 4 \times 0.5 = 4$ units.

29. What is the unit of angular momentum in the SI system?

    Kilogram meter squared per second ($\text{kg} \cdot \text{m}^2/\text{s}$). Derived from $L = mvr$ with standard SI base units.

30. How does doubling the mass of a rotating object affect its angular momentum?

    Angular momentum doubles. Since $L = I\omega$ and $I = mr^2$, doubling $m$ doubles $L$.

31. How does angular momentum conservation apply to a collapsing star?

    Angular velocity increases as the star's radius decreases. Conservation requires $\omega$ to increase as radius shrinks.

32. Define moment of inertia for a point mass.

    $I = mr^2$. Mass times distance squared from rotation axis.

33. What condition must be met for angular momentum to be conserved?

    No net external torque. Zero net torque is required for conservation.

34. What is the effect of decreasing radius on angular velocity if $L$ is constant?

    Angular velocity increases. Since $L = I\omega = mr^2\omega$, smaller $r$ requires larger $\omega$.

35. What happens to angular momentum when net external torque is applied?

    Angular momentum changes. External torque causes rate of change in angular momentum.

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