Circular Motion - AP Physics 1

1. Define radial acceleration.

   Acceleration towards the center of circular path. Same as centripetal acceleration definition.

2. State the formula for angular velocity.

   $\omega = \frac{\Delta\theta}{\Delta t}$. Change in angle divided by time interval.

3. Describe the relationship between frequency and angular velocity.

   $\omega = 2\pi f$. One revolution equals $2\pi$ radians.

4. What is the relationship between period and angular velocity?

   $\omega = \frac{2\pi}{T}$. One complete revolution takes period $T$.

5. What is centripetal acceleration?

   Acceleration directed towards the center of circular path. Always points inward, creating circular motion.

6. Calculate angular velocity: $T=3$ s.

   $\frac{2\pi}{3}$ rad/s. Using $\omega = 2\pi/T = 2\pi/3$ rad/s.

7. Find frequency: $T=0.1$ s.

   $10$ Hz. Using $f = 1/T = 1/0.1 = 10$ Hz.

8. Calculate tangential velocity: $r=3$ m, $\omega=2$ rad/s.

   $6$ m/s. Using $v = r\omega = 3 \times 2 = 6$ m/s.

9. Find radius given $v=6$ m/s, $a_c=9$ m/s².

   $4$ m. Using $r = v^2/a_c = 6^2/9 = 4$ m.

10. Define period in circular motion.

    Time to complete one full revolution. Complete cycle duration in circular motion.

11. Identify the cause of centripetal acceleration.

    Change in direction of velocity. Velocity direction changes continuously in circles.

12. Find the period given frequency of 2 Hz.

    0.5 s. Using $T = 1/f = 1/2 = 0.5$ s.

13. State the formula for angular displacement.

    $\theta = \omega t$. Angle equals angular velocity times time.

14. State the relationship between period and frequency.

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

15. Find angular velocity: $\theta=\pi/2$ rad, $t=2$ s.

    $\pi/4$ rad/s. Using $\omega = \theta/t = (\pi/2)/2 = \pi/4$ rad/s.

16. What is angular velocity?

    Rate of change of angular displacement. How fast angle changes with time.

17. Find centripetal acceleration: $v=10$ m/s, $r=5$ m.

    $20$ m/s². Using $a_c = v^2/r = 10^2/5 = 20$ m/s².

18. What is the formula for tangential velocity?

    $v = r\omega$. Same as linear velocity for circular motion.

19. What is tangential velocity?

    Velocity tangent to the circular path. Speed along the circular path's edge.

20. Calculate period: $f=0.5$ Hz.

    $2$ s. Using $T = 1/f = 1/0.5 = 2$ s.

21. What is uniform circular motion?

    Motion in a circle with constant speed. Constant speed but changing direction.

22. What is the direction of centripetal force?

    Towards the center of the circular path. Always points inward to maintain circular path.

23. State the formula for centripetal force.

    $F_c = \frac{mv^2}{r}$. Newton's second law applied to circular motion.

24. Identify the force responsible for circular motion.

    Centripetal force. Net inward force maintains circular path.

25. Calculate centripetal acceleration: $v=4$ m/s, $r=2$ m.

    $8$ m/s². Using $a_c = v^2/r = 4^2/2 = 8$ m/s².

26. What is the relationship between tangential speed and radius?

    Directly proportional. Larger radius gives higher tangential speed.

27. Calculate centripetal force: $m=2$ kg, $v=3$ m/s, $r=1$ m.

    $18$ N. Using $F_c = mv^2/r = 2(3^2)/1 = 18$ N.

28. Calculate period: $f=5$ Hz.

    $0.2$ s. Using $T = 1/f = 1/5 = 0.2$ s.

29. What is the effect of increasing radius on centripetal force?

    Decreases centripetal force for constant velocity. Force inversely proportional to radius.

30. What is the unit of angular velocity?

    Radians per second (rad/s). Standard unit for rotational speed.

31. State the formula for centripetal acceleration.

    $a_c = \frac{v^2}{r}$. Speed squared divided by radius gives centripetal acceleration.

32. Calculate frequency: $T=0.25$ s.

    $4$ Hz. Using $f = 1/T = 1/0.25 = 4$ Hz.

33. Find the force: $m=3$ kg, $a_c=4$ m/s².

    $12$ N. Using $F = ma = 3 \times 4 = 12$ N.

34. Define angular displacement.

    Angle through which a point or line is rotated. Measures rotational position change.

35. Define frequency in circular motion.

    Number of revolutions per unit time. How many cycles occur per second.

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