Rotational Equilibrium and Newton's First Law - AP Physics 1

1. State the principle of superposition for torques.

   The net torque is the vector sum of all individual torques. Individual torques add vectorially.

2. State the formula for angular velocity.

   $\text{Angular velocity} (\text{rad/s}) = \frac{\text{Change in angle}}{\text{Change in time}}$. Rate of angular position change.

3. What is the effect of torque on an object's rotational state?

   Changes the object's angular velocity. Torque causes rotational acceleration or deceleration.

4. Identify the formula for the lever arm.

   Lever arm $= r \times \text{sin}(\theta)$. Perpendicular distance from force line to axis.

5. State the relationship between torque and angular acceleration.

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

6. What happens to angular velocity if net torque is applied?

   Angular velocity changes. Net torque causes angular acceleration.

7. Find the net torque if $\tau_1 = 5 \text{N·m}$ and $\tau_2 = -3 \text{N·m}$.

   Net torque = $2 \text{N·m}$. Vector sum: $5 + (-3) = 2$.

8. Identify the direction of the torque vector.

   Perpendicular to the plane formed by $r$ and $F$. Right-hand rule determines direction.

9. Identify the symbol for angular velocity.

   $\text{omega} (\text{ω})$. Greek letter representing angular velocity.

10. What is the condition for an object to be in static rotational equilibrium?

    Net torque and net force must both be zero. No linear or rotational acceleration.

11. Which direction does positive torque rotate an object?

    Counterclockwise. Standard convention for positive rotation.

12. What is the effect of increasing the distance $r$ in the torque formula?

    Increases torque, if force and angle remain constant. Torque is proportional to radius.

13. State the condition for equilibrium of a rotational system.

    Sum of all external torques must be zero. Rotational equilibrium requires balanced torques.

14. Which quantity remains constant for an object in rotational equilibrium?

    Angular velocity remains constant. No net torque means constant rotation.

15. What is the rotational kinetic energy formula?

    $KE_{\text{rotational}} = \frac{1}{2} I \times \text{ω}^2$. Rotational analog of $\frac{1}{2}mv^2$.

16. What is the rotational analog of force in linear motion?

    Torque ($\tau$). Rotational equivalent of linear force.

17. State the formula for moment of inertia of a point mass.

    $I = m \times r^2$. Mass times distance squared from axis.

18. How does increasing the force $F$ affect the torque?

    Increases torque, if $r$ and $\theta$ remain constant. Torque is proportional to applied force.

19. Identify the unit of torque in SI units.

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

20. If moment of inertia increases, what happens to angular acceleration?

    Angular acceleration decreases. From $\tau = I\alpha$, larger $I$ means smaller $\alpha$.

21. In rotational motion, what does $\theta$ represent?

    Angular displacement. Angle rotated from reference position.

22. What is the role of the pivot point in torque calculations?

    Acts as the reference point for distance and direction. Axis about which rotation and distances measured.

23. Find the torque if $r = 3 \text{m}$, $F = 4 \text{N}$, $\theta = 90^\text{o}$.

    $\tau = 12 \text{N·m}$. $\tau = 3 \times 4 \times \sin(90°) = 12$.

24. What is the unit of angular displacement?

    Radians (rad). Standard unit for angle measurement.

25. What happens to torque if the angle $\theta = 0^\text{o}$?

    Torque is zero. Force parallel to radius produces no rotation.

26. State Newton's First Law in rotational form.

    An object remains at rest or in uniform rotation unless acted upon by a net external torque. Rotational version of inertia law.

27. What is the formula for angular acceleration?

    $\text{Angular acceleration} (\text{α}) = \frac{\text{Change in angular velocity}}{\text{Change in time}}$. Rate of angular velocity change.

28. What happens to an object in rotational equilibrium if external torque is applied?

    It will begin to rotate. Equilibrium breaks, causing angular acceleration.

29. Identify the variable representing angular displacement.

    $\theta$. Symbol for angular position measurement.

30. Identify the factor that torque depends on besides force.

    Distance from pivot point and angle of force. Radius and angle determine lever arm effectiveness.

31. What is the condition for equilibrium of a seesaw?

    Sum of clockwise torques = Sum of counterclockwise torques. Torques must balance for equilibrium.

32. Find the angular acceleration if $I = 2 \text{kg·m}^2$ and $\tau = 4 \text{N·m}$.

    $\text{α} = 2 \text{rad/s}^2$. Using $\alpha = \tau/I = 4/2 = 2$.

33. What is the relationship between torque and rotational inertia?

    Torque causes rotational inertia to change angular velocity. Torque overcomes inertia to change motion.

34. What is torque's formula?

    $\tau = r \times F \times \text{sin}(\theta)$. Force times perpendicular distance from axis.

35. What is the condition for rotational equilibrium?

    Net torque ($\tau_{\text{net}}$) must be zero. No angular acceleration occurs when forces balance.

36. If $\tau = 0$, what can be inferred about the object's rotation?

    The object is either at rest or in uniform rotation. Newton's first law for rotation applies.

37. Which direction does negative torque rotate an object?

    Clockwise. Standard convention for negative rotation.

38. What is the rotational analog of mass?

    Moment of inertia ($I$). Resistance to rotational motion.

39. What is the significance of the angle $\theta$ in torque calculations?

    Determines the component of force causing rotation. Only perpendicular force component creates torque.

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