Torque - AP Physics 1

1. State the effect on torque if $\theta$ changes from $90^\circ$ to $0^\circ$.

   Torque decreases to zero. Maximum torque at $90°$ reduces to zero at $0°$.

2. What happens to torque if the angle is decreased from $90^\circ$?

   Torque decreases. Smaller angles reduce $\sin(\theta)$, decreasing rotational effect.

3. Calculate torque for $r=3$ m, $F=10$ N, $\theta=60^\circ$.

   $\tau = 25.98$ Nm. $\tau = 3 \times 10 \times \sin(60°) = 30 \times 0.866 = 25.98$ Nm.

4. What is the effect of perpendicular force application on torque?

   Maximizes torque. Perpendicular application gives $\sin(90°) = 1$, the maximum value.

5. Which direction is positive torque conventionally?

   Counterclockwise. Standard physics convention for positive rotational direction.

6. Identify the unit of torque in the SI system.

   Newton-meter (Nm). Force times distance gives units of energy per radian.

7. Choose the result when a force acts at the pivot point.

   Torque is zero. At the pivot point, the lever arm distance $r = 0$.

8. What is the effect of negative torque on rotation?

   Causes clockwise rotation. Negative torque produces rotation opposite to positive direction.

9. State the torque if $F=8$ N, $r=0.5$ m, and $\theta=90^\circ$.

   $\tau = 4$ Nm. $\tau = 8 \times 0.5 \times \sin(90°) = 8 \times 0.5 \times 1 = 4$ Nm.

10. Identify the symbol for torque in equations.

    $\tau$. Greek letter tau is the standard physics symbol for torque.

11. What does $r$ represent in the torque formula?

    Distance from pivot point to force application. The lever arm length determines how much turning advantage you have.

12. Find the torque for $r=2$ m, $F=5$ N, $\theta=30^\circ$.

    $\tau = 5$ Nm. $\tau = 2 \times 5 \times \sin(30°) = 2 \times 5 \times 0.5 = 5$ Nm.

13. When is the torque zero?

    When $\theta = 0^\circ$ or $\sin(\theta) = 0$. Force parallel to lever arm produces no rotational effect.

14. What is the torque if $F=0$?

    Zero. No force means no rotational effect can be produced.

15. Identify the direction of torque for negative angle.

    Clockwise. Negative angles conventionally indicate clockwise rotation direction.

16. State the effect of doubling $r$ on torque if $F$ and $\theta$ are constant.

    Torque doubles. Torque is directly proportional to lever arm length.

17. What happens to torque if the force increases?

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

18. State the effect on torque if the force is perpendicular to the lever arm.

    Torque is maximized. Perpendicular force gives $\sin(90°) = 1$, the maximum torque.

19. What is the formula for torque?

    $\tau = r \cdot F \cdot \sin(\theta)$. Fundamental formula where all three factors determine rotational effect.

20. Which quantity is vector: force, mass, or torque?

    Torque. Torque has both magnitude and direction, making it a vector.

21. What is the net torque if equal and opposite torques are applied?

    Zero. Equal magnitude opposite torques cancel each other out.

22. What is the torque if $r=0$?

    Zero. No lever arm means no rotational advantage or effect.

23. Calculate torque for $r=1.5$ m, $F=20$ N, $\theta=45^\circ$.

    $\tau = 21.21$ Nm. $\tau = 1.5 \times 20 \times \sin(45°) = 30 \times 0.707 = 21.21$ Nm.

24. Choose the effect of increasing $r$ on torque.

    Torque increases. Torque is directly proportional to lever arm distance.

25. State the right-hand rule in torque context.

    Curl fingers in rotation direction; thumb points in torque direction. Standard method to determine torque vector direction in 3D.

26. What is the torque direction for a positive angle?

    Counterclockwise. Positive angles correspond to counterclockwise rotation by convention.

27. Identify the factor that does not affect torque.

    Mass of the object. Mass affects weight but not the geometric torque relationship.

28. What does $F$ represent in the torque formula?

    Magnitude of the force applied. The force magnitude directly affects the rotational strength.

29. Find the angle for zero torque if $r=4$ m and $F=7$ N.

    $\theta = 0^\circ$ or $180^\circ$. When force is parallel to lever arm, $\sin(\theta) = 0$.

30. Find the net torque: $\tau_1=5$ Nm, $\tau_2=-3$ Nm.

    $\tau_{net} = 2$ Nm. Vector addition: $5 + (-3) = 2$ Nm in positive direction.

31. What does $\tau$ represent in the torque formula?

    Torque. Greek letter tau represents the rotational moment or turning effect.

32. What does $\theta$ represent in the torque formula?

    Angle between force and lever arm. This angle determines the effective component of force causing rotation.

33. Calculate the torque if $r=2$ m, $F=10$ N, $\theta=0^\circ$.

    $\tau = 0$ Nm. $\sin(0°) = 0$, so torque equals zero regardless of $r$ and $F$.

34. Find torque: $r=3$ m, $F=15$ N, $\theta=90^\circ$.

    $\tau = 45$ Nm. $\tau = 3 \times 15 \times \sin(90°) = 3 \times 15 \times 1 = 45$ Nm.

35. Find the lever arm if torque is $20$ Nm and force is $5$ N.

    $r = 4$ m. From $\tau = rF\sin(\theta)$, assuming $\theta = 90°$: $r = \tau/F = 20/5 = 4$ m.

36. Calculate torque: $r=1$ m, $F=10$ N, $\theta=45^\circ$.

    $\tau = 7.07$ Nm. $\tau = 1 \times 10 \times \sin(45°) = 10 \times 0.707 = 7.07$ Nm.

37. State the relationship between torque and rotational equilibrium.

    Net torque must be zero. No net torque means no angular acceleration occurs.

38. What effect does increasing $\theta$ to $90^\circ$ have on torque?

    Torque increases. Approaching $90^\circ$ increases $\sin(\theta)$ toward its maximum value.

39. State the condition for maximum torque.

    $\theta = 90^\circ$ or $\sin(\theta) = 1$. Perpendicular force application maximizes the rotational effect.

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