Torque and Work - AP Physics 1

1. Calculate work: $F = 10 \text{ N}$, $d = 4 \text{ m}$, $\theta = 0°$.

   $W = 40 \text{ J}$. $W = 10 \times 4 \times \cos(0°) = 40$ J.

2. Define the term 'moment arm' in physics.

   Another term for lever arm. Moment arm and lever arm are synonymous terms in rotational mechanics.

3. Find the torque if a force of 10 N is applied 2 m from pivot at 90°.

   $\tau = 20 \text{ N·m}$. $\tau = 10 \times 2 \times \sin(90°) = 20$ N·m.

4. State the SI unit for work.

   Joule (J). Work is energy transfer, measured in joules (force × distance).

5. What is the effect of a force with no lever arm on torque?

   Produces zero torque. Zero lever arm means the force passes through the rotation axis.

6. What is the formula for torque ($\tau$) in terms of force and lever arm?

   $\tau = r \cdot F \cdot \sin(\theta)$. Where $r$ is lever arm, $F$ is force magnitude, and $\theta$ is angle between force and lever arm.

7. Calculate power: $W = 200 \text{ J}$, $t = 5 \text{ s}$.

   $P = 40 \text{ W}$. $P = \frac{200}{5} = 40$ W.

8. Which angle maximizes torque for a given force and lever arm?

   90 degrees or $\frac{\pi}{2}$ radians. Maximum torque occurs when force is perpendicular to lever arm ($\sin(90°) = 1$).

9. Calculate the torque: $F = 15 \text{ N}$, $r = 3 \text{ m}$, $\theta = 30°$.

   $\tau = 22.5 \text{ N·m}$. $\tau = 15 \times 3 \times \sin(30°) = 45 \times 0.5 = 22.5$ N·m.

10. What is the rotational equivalent of mass in linear motion?

    Moment of inertia. Moment of inertia measures resistance to angular acceleration.

11. Identify the condition for equilibrium in terms of net torque.

    Net torque must be zero. No net rotation occurs when clockwise and counterclockwise torques balance.

12. Define lever arm in the context of torque.

    Perpendicular distance from axis of rotation to line of action of force. The shortest distance determines the effectiveness of the applied force.

13. Calculate the work done by a 5 N force over 3 m in the same direction.

    $W = 15 \text{ J}$. $W = 5 \times 3 \times \cos(0°) = 15$ J.

14. What is the formula for rotational work?

    $W = \tau \cdot \theta$. Where $\tau$ is torque and $\theta$ is angular displacement in radians.

15. What is the formula for gravitational potential energy?

    $U = mgh$. Potential energy depends on mass, gravity, and height above reference.

16. What is the effect of zero net torque on an object's rotation?

    No change in rotational motion. Zero net torque means constant angular velocity (including zero).

17. State the formula for power in terms of work and time.

    $P = \frac{W}{t}$. Power equals work divided by the time taken to do that work.

18. How is net work related to net force?

    Net work is done by net force. Net work is the sum of work done by all forces acting.

19. What is the relationship between force and torque?

    Torque is the rotational equivalent of force. Torque causes rotation just as force causes linear acceleration.

20. What is the condition for mechanical equilibrium?

    Net force and net torque must both be zero. Object neither translates nor rotates when all forces and torques balance.

21. What is the angular displacement in work done by torque?

    The angle through which the object rotates. Angular displacement $\theta$ must be measured in radians for the work formula.

22. If $\theta = 0°$, what is $\cos(\theta)$ in the work formula?

    $\cos(\theta) = 1$. When force and displacement are parallel, maximum work is done.

23. How does torque affect rotational motion?

    Causes angular acceleration. Net torque produces angular acceleration according to $\tau = I\alpha$.

24. What is the formula for instantaneous power in terms of force and velocity?

    $P = F \cdot v \cdot \cos(\theta)$. Where $v$ is velocity and $\theta$ is angle between force and velocity vectors.

25. State the work-energy principle.

    Work done on an object equals change in kinetic energy. Net work equals the change in kinetic energy of the object.

26. What is the effect of torque on angular velocity?

    Changes angular velocity. Torque causes angular acceleration, which changes angular velocity over time.

27. State the unit of torque in the International System of Units (SI).

    Newton meter (N·m). Torque combines force and distance, so units are force × distance.

28. State the principle of conservation of mechanical energy.

    Total mechanical energy remains constant if only conservative forces act. Energy converts between kinetic and potential but total stays constant.

29. What is the formula for kinetic energy?

    $KE = \frac{1}{2}mv^2$. Kinetic energy depends on mass and the square of velocity.

30. What happens to torque if the lever arm is doubled?

    Torque is doubled. Torque is directly proportional to lever arm in the formula.

31. If power is 50 W and time is 2 s, what is the work done?

    $W = 100 \text{ J}$. $W = P \times t = 50 \times 2 = 100$ J.

32. Calculate gravitational work: $m = 2 \text{ kg}$, $g = 9.8 \text{ m/s}^2$, $h = 5 \text{ m}$.

    $W = 98 \text{ J}$. $W = mgh = 2 \times 9.8 \times 5 = 98$ J.

33. What is the formula for work done by a constant force?

    $W = F \cdot d \cdot \cos(\theta)$. Where $F$ is force, $d$ is displacement, and $\theta$ is angle between them.

34. Identify the rotational analog of Newton's second law.

    $\tau = I\alpha$. Relates torque to moment of inertia and angular acceleration.

35. What is the work done by a force perpendicular to displacement?

    Zero. Perpendicular force means $\theta = 90°$, so $\cos(90°) = 0$.

36. What is the relationship between work and energy?

    Work is the transfer of energy. Work changes an object's kinetic or potential energy state.

37. Identify the unit of measure for power in the SI system.

    Watt (W). Power is energy per unit time, so watts = joules/second.

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