Torque and Work - AP Physics C Mechanics

1. What is the formula for impulse?

   $J = \Delta p = F\Delta t$. Change in momentum equals force times time.

2. State the unit of torque in the SI system.

   Newton-meter (N·m). Force times distance unit.

3. What is the formula for centripetal force?

   $F_c = \frac{mv^2}{r}$. Inward force for circular motion.

4. State the work-energy principle.

   Net work done equals change in kinetic energy. Fundamental theorem connecting work and motion.

5. Find the torque if $r = 2\, \text{m}$, $F = 5\, \text{N}$, $\theta = 90^\circ$.

   $\tau = 10\, \text{N} \cdot \text{m}$. Force perpendicular to lever arm maximizes torque.

6. What is the condition for equilibrium in terms of torque?

   Net torque must be zero. Sum of all torques equals zero for equilibrium.

7. What is the definition of a conservative force?

   A force with work independent of path taken. Gravity and springs are conservative forces.

8. What is the formula for the efficiency of a machine?

   $\text{Efficiency} = \frac{\text{Useful Work Output}}{\text{Total Work Input}} \times 100\%$. Ratio of useful output to total input.

9. Define the term 'lever arm' in the context of torque.

   Perpendicular distance from axis of rotation to line of action of force. Distance that determines torque magnitude.

10. Identify the unit of work in the SI system.

    Joule (J). Newton-meter equals one joule.

11. What is the definition of power in terms of energy?

    Rate of energy transfer or conversion. How quickly energy is transformed.

12. What is the formula for power in terms of work and time?

    $P = \frac{W}{t}$. Rate at which work is done.

13. Calculate the linear momentum of a $3\, \text{kg}$ object moving at $4\, \text{m/s}$.

    $p = 12\, \text{kg} \cdot \text{m/s}$. Product of mass and velocity.

14. What is rotational kinetic energy?

    $KE_{rot} = \frac{1}{2}I\omega^2$. Rotational analog of translational kinetic energy.

15. Calculate the gravitational potential energy for a $5\, \text{kg}$ object at $10\, \text{m}$ height.

    $PE = 490\, \text{J}$. Mass times gravitational acceleration times height.

16. Define the term 'moment of inertia'.

    Resistance of an object to changes in its rotational motion. Rotational inertia about an axis.

17. What is the formula for work done by a variable force?

    $W = \int F(x) \, dx$. Integration accounts for varying force magnitude.

18. What is the formula for gravitational potential energy?

    $PE = mgh$. Energy due to position in gravitational field.

19. What does $\theta$ represent in the torque formula $\tau = r \times F \times \sin(\theta)$?

    Angle between force vector and lever arm. Determines effective component of force for torque.

20. What is the principle of conservation of mechanical energy?

    Total mechanical energy remains constant if only conservative forces act. Sum of kinetic and potential energy stays constant.

21. Find the work done if a force of $20\, \text{N}$ moves an object $4\, \text{m}$ in the direction of force.

    $W = 80\, \text{J}$. Force and displacement in same direction.

22. Calculate the work done when a force of $10\, \text{N}$ acts over $3\, \text{m}$ at $30^\circ$.

    $W = 25.98\, \text{J}$. Force component parallel to displacement does work.

23. Identify the unit of power in the SI system.

    Watt (W). Joule per second equals one watt.

24. State the formula for calculating the net work done on an object.

    $W_{net} = \Delta KE = \frac{1}{2}mv^2_f - \frac{1}{2}mv^2_i$. Net work equals change in kinetic energy.

25. What is the formula for rotational work?

    $W = \tau \times \Delta \theta$. Rotational analog of $W = F \times d$.

26. What is the relationship between torque and angular acceleration?

    $\tau = I\alpha$. Rotational analog of Newton's second law.

27. Calculate the power if $150\, \text{J}$ of work is done in $10\, \text{s}$.

    $P = 15\, \text{W}$. Work divided by time interval.

28. What is the relationship between work and energy?

    Work is the transfer of energy. Work changes the energy state of a system.

29. Find the impulse when a force of $10\, \text{N}$ acts for $5\, \text{s}$.

    $J = 50\, \text{N} \cdot \text{s}$. Force multiplied by time interval.

30. What is the formula for torque in terms of force and distance?

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

31. State the formula for angular momentum.

    $L = I\omega$. Rotational momentum for spinning objects.

32. What is the formula for kinetic energy?

    $KE = \frac{1}{2}mv^2$. Energy of motion for translational movement.

33. What is the formula for linear momentum?

    $p = mv$. Mass times velocity vector.

34. Calculate the potential energy in a spring with $k = 200\, \text{N/m}$ and $x = 0.1\, \text{m}$.

    $PE = 1\, \text{J}$. Spring constant times displacement squared.

35. State the formula for the potential energy stored in a spring.

    $PE_{spring} = \frac{1}{2}kx^2$. Elastic potential energy in compressed spring.

36. Which physical quantity is conserved in the absence of external torques?

    Angular momentum. Rotational momentum is conserved without external torques.

37. Find the change in kinetic energy if a $2\, \text{kg}$ object speeds from $3\, \text{m/s}$ to $5\, \text{m/s}$.

    $\Delta KE = 16\, \text{J}$. Final kinetic energy minus initial kinetic energy.

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

    $W = F \times d \times \cos(\theta)$. Dot product of force and displacement vectors.

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