Torque - AP Physics C Mechanics

1. Describe the effect of torque on an object's rotation.

   Changes angular velocity. Torque produces angular acceleration per Newton's second law.

2. What is the result of applying equal and opposite torques?

   No net torque. Equal magnitudes in opposite directions cancel out.

3. Define torque in terms of rotational motion.

   Torque is the rotational equivalent of force. It causes rotational motion like force causes linear motion.

4. State the equation relating torque to power in rotational motion.

   $P = \tau \cdot \omega$. Rotational power equals torque times angular velocity.

5. What is the effect of increasing the lever arm on torque?

   Increases torque. Longer lever arm multiplies the rotational effect.

6. Calculate torque for $F = 50\,\text{N}$, $r = 0.8\,\text{m}$, $\theta = 30^{\circ}$.

   $20\,\text{N}\cdot\text{m}$. $\tau = 50 \times 0.8 \times \sin(30°) = 40 \times 0.5$

7. Identify the direction of torque caused by a counterclockwise force.

   Positive torque. Counterclockwise is conventionally positive.

8. What factor of torque is zero if force is applied at the pivot point?

   Lever arm distance. Distance from pivot is the key factor.

9. What is the formula for torque?

   $\tau = r \times F \times \sin(\theta)$. Cross product of position vector and force vector.

10. What happens to torque if the force is doubled?

    Torque doubles. Torque is directly proportional to applied force.

11. Find the torque: $F = 10\,\text{N}$, $r = 0.5\,\text{m}$, $\theta = 90^{\circ}$.

    $5\,\text{N}\cdot\text{m}$. $\tau = 10 \times 0.5 \times 1 = 5$

12. What is the torque if the force is applied at the pivot?

    Zero. Lever arm distance is zero at the pivot.

13. State the relationship between torque and angular acceleration.

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

14. Calculate torque: $F = 25\,\text{N}$, $r = 2\,\text{m}$, $\theta = 30^{\circ}$.

    $25\,\text{N}\cdot\text{m}$. $\tau = 25 \times 2 \times \sin(30°) = 50 \times 0.5$

15. Find torque: $F = 20\,\text{N}$, $r = 3\,\text{m}$, $\theta = 45^{\circ}$.

    $30\sqrt{2}\,\text{N}\cdot\text{m}$. $\tau = 20 \times 3 \times \sin(45°) = 60 \times \frac{\sqrt{2}}{2}$

16. Identify the units of torque in the SI system.

    Newton-meters (N·m). Force times distance has these units.

17. Define the lever arm in a torque context.

    Perpendicular distance from pivot to line of action. The effective distance that matters for rotation.

18. State the principle of superposition for torque.

    Net torque is the sum of individual torques. Torques add vectorially like forces do.

19. What is the torque if the force is perpendicular to the lever arm?

    $\tau = r \cdot F$. Simplified formula when $\sin(90°) = 1$.

20. What role does $\theta$ play in calculating torque?

    Determines effectiveness of force. Angle controls the component of force causing rotation.

21. Calculate torque for $r = 1\,\text{m}$, $F = 10\,\text{N}$, $\theta = 0^{\circ}$.

    Zero torque. $\sin(0°) = 0$ eliminates rotational effect.

22. What is the effect of a negative torque value?

    Causes clockwise rotation. Negative indicates clockwise direction by convention.

23. What happens to torque if the distance from pivot doubles?

    Torque doubles. Torque is directly proportional to lever arm.

24. State the condition for rotational equilibrium.

    Net torque is zero. Sum of all torques equals zero for no rotation.

25. Calculate torque with $r = 2\,\text{m}$, $F = 5\,\text{N}$, $\theta = 60^{\circ}$.

    $5\sqrt{3}\,\text{N}\cdot\text{m}$. $\tau = 2 \times 5 \times \sin(60°) = 10 \times \frac{\sqrt{3}}{2}$

26. Determine the net torque: $\tau_1 = 5\,\text{N}\cdot\text{m}$, $\tau_2 = -3\,\text{N}\cdot\text{m}$.

    $2\,\text{N}\cdot\text{m}$. Add torques algebraically: $5 + (-3) = 2$

27. What does a zero net torque imply about rotational motion?

    No angular acceleration. From $\tau = I\alpha$, if $\tau = 0$ then $\alpha = 0$.

28. Explain the effect of torque on a rolling object.

    Causes angular acceleration. Torque creates rotational motion in rolling objects.

29. What is the effect of force magnitude on torque?

    Torque increases with force magnitude. Torque is directly proportional to force.

30. Identify the pivot point in a torque problem.

    The point about which the object rotates. The axis or fulcrum about which rotation occurs.

31. How does torque change if force direction is parallel to lever arm?

    Torque is zero. $\sin(0°) = 0$ makes torque zero.

32. What is the relationship between torque and rotational work?

    $W = \tau \cdot \Delta \theta$. Work is torque times angular displacement.

33. Find torque: $F = 15\,\text{N}$, $r = 4\,\text{m}$, $\theta = 90^{\circ}$.

    $60\,\text{N}\cdot\text{m}$. $\tau = 15 \times 4 \times 1 = 60$

34. What angle $\theta$ maximizes torque for a given force?

    $90^{\circ}$. $\sin(90°) = 1$ gives maximum value.

35. What is the significance of the moment of inertia in torque?

    It resists angular acceleration. Higher inertia requires more torque for same acceleration.

36. How does an increase in moment of inertia affect angular acceleration?

    Decreases angular acceleration. From $\tau = I\alpha$, larger $I$ gives smaller $\alpha$.

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