Circular Motion - AP Physics C Mechanics

1. Define angular velocity.

   Rate of change of angular displacement. Rate at which angular displacement changes with time.

2. Find the angular displacement after 2 seconds if $\text{ω} = 3 \text{ rad/s}$.

   $\theta = 6 \text{ rad}$. Using $\theta = \omega t = 3 \times 2 = 6$ radians.

3. Identify the direction of centripetal acceleration.

   Towards the center of the circle. Centripetal acceleration always points radially inward.

4. Calculate angular velocity for 3 revolutions in 6 seconds.

   $\text{ω} = \frac{\text{π}}{1} \text{ rad/s}$. Using $\omega = \frac{2\pi \times 3}{6} = \pi$ rad/s.

5. What is angular displacement?

   The angle through which an object moves on a circular path. Angular measure of rotational motion in radians.

6. What is the direction of angular velocity vector?

   Perpendicular to the plane of rotation. Angular velocity vector follows right-hand rule convention.

7. Find the centripetal force for a 5 kg mass moving at 3 m/s in a 2 m radius circle.

   $F_c = 22.5 \text{ N}$. Using $F_c = \frac{mv^2}{r} = \frac{5 \times 9}{2} = 22.5$ N.

8. What is the formula for the radial component of acceleration in circular motion?

   $a_r = \frac{v^2}{r}$. Radial acceleration component points toward the center of curvature.

9. What is the formula for centripetal acceleration?

   $a_c = \frac{v^2}{r}$. Acceleration directed toward the center, proportional to $v^2$ and inversely to radius.

10. State the relationship between period (T) and frequency (f).

    $T = \frac{1}{f}$. Period and frequency are reciprocals of each other.

11. Determine the angular velocity if $v = 10 \text{ m/s}$ and $r = 2 \text{ m}$.

    $\text{ω} = 5 \text{ rad/s}$. Using $\omega = \frac{v}{r} = \frac{10}{2} = 5$ rad/s.

12. Define the term 'period' in circular motion.

    Time taken for one complete revolution. Time required for object to complete one full circular path.

13. What is the unit of angular acceleration in the SI system?

    Radians per second squared (rad/s²). Standard SI unit for rate of change of angular velocity.

14. What is the symbol for angular displacement?

    θ (theta). Greek letter theta represents angular displacement in physics.

15. What is the formula for angular displacement?

    $\theta = \frac{s}{r}$. Angle equals arc length divided by radius.

16. What is the formula for angular momentum, $L$?

    $L = I\text{ω}$. Angular momentum equals moment of inertia times angular velocity.

17. Identify the force that acts as centripetal force in a car taking a turn.

    Frictional force. Friction between tires and road provides the centripetal force.

18. What is the unit of moment of inertia in the SI system?

    Kilogram meter squared (kg·m²). Standard SI unit for rotational inertia measurement.

19. State the formula for centripetal force.

    $F_c = \frac{mv^2}{r}$. Force equals mass times centripetal acceleration.

20. Which physical quantity remains constant in uniform circular motion?

    Speed. Speed magnitude is constant while direction continuously changes.

21. What is the unit of angular velocity in the SI system?

    Radians per second (rad/s). Standard SI unit for rate of angular change per time.

22. What is the formula for net torque?

    $\tau_{\text{net}} = I α$. Net torque equals moment of inertia times angular acceleration.

23. Calculate the period for a frequency of $0.5 \text{ Hz}$.

    $T = 2 \text{ s}$. Using $T = \frac{1}{f} = \frac{1}{0.5} = 2$ seconds.

24. What is the formula for the linear speed, $v$, in terms of angular speed, $ω$?

    $v = rω$. Linear speed equals radius times angular speed.

25. What is the formula for angular velocity in terms of period?

    $ω = \frac{2π}{T}$. Angular velocity equals $2π$ radians divided by period.

26. Which axis is the angular velocity vector aligned with for a wheel rotating in the xy-plane?

    z-axis. Right-hand rule determines angular velocity vector direction.

27. State the formula for moment of inertia, $I$, of a point mass.

    $I = mr^2$. Moment of inertia equals mass times radius squared for point mass.

28. What is the centripetal acceleration of an object moving at 4 m/s in a circle of radius 2 m?

    $a_c = 8 \text{ m/s}^2$. Using $a_c = \frac{v^2}{r} = \frac{4^2}{2} = 8 \text{ m/s}^2$.

29. Calculate the frequency if the period is 5 seconds.

    $f = 0.2 \text{ Hz}$. Using $f = \frac{1}{T} = \frac{1}{5} = 0.2$ Hz.

30. State the formula for tangential acceleration.

    $a_t = r\text{α}$. Tangential acceleration equals radius times angular acceleration.

31. What is the relationship between torque and angular momentum?

    $\tau = \frac{dL}{dt}$. Torque equals the time rate of change of angular momentum.

32. What is the formula for frequency in terms of angular velocity?

    $f = \frac{\omega}{2\pi}$. Frequency equals angular velocity divided by $2\pi$.

33. Define centripetal force.

    Force directed towards the center of circular motion. Net force that maintains circular motion by pulling inward.

34. Identify the formula for period in circular motion.

    $T = \frac{2\text{π}r}{v}$. Time for one complete revolution equals circumference divided by speed.

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

    $\tau = I\text{α}$. Torque equals moment of inertia times angular acceleration.

36. Which force provides the centripetal force in a satellite orbit?

    Gravitational force. Gravity provides the centripetal force for orbital motion.

37. State the formula that relates net force to centripetal acceleration.

    $F_{\text{net}} = ma_c$. Newton's second law applied to circular motion dynamics.

38. What is the formula for the gravitational force acting as centripetal force in orbit?

    $F_g = \frac{Gm_1m_2}{r^2}$. Newton's universal gravitation law for orbital mechanics.

39. Determine the linear velocity of a point on a wheel with radius 0.5 m and $ω = 10 \text{ rad/s}$.

    $v = 5 \text{ m/s}$. Using $v = r\omega = 0.5 \times 10 = 5$ m/s.

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