Uniform circular motion (kinematics) Knowledge-Based Practice

Questions

1. 1.

   A particle moves in uniform circular motion along a circular path of radius $R$. What is the ratio of the distance traveled by the particle to the magnitude of its displacement after completing half of a revolution?

   • A) 1
   • B) $\frac{2}{\pi}$
   • C) $\pi$
   • D) $\frac{\pi}{2}$
2. 2.

   An object moves in uniform circular motion with a centripetal acceleration of magnitude $a$. If the linear speed of the object is doubled and the radius of its circular path is halved, what is the new magnitude of its centripetal acceleration?

   • A) $2a$
   • B) $4a$
   • C) $8a$
   • D) $16a$
3. 3.

   A particle moves in uniform circular motion along a circular path of radius 0.60 m. If the particle sweeps through a central angle of 4.0 rad in 2.0 s, what is the linear speed of the particle?

   • A) 3.3 m/s
   • B) 2.0 m/s
   • C) 2.4 m/s
   • D) 1.2 m/s
4. 4.

   A particle moves in uniform circular motion along a circular path of radius $R$. What is the magnitude of the particle's displacement after it completes three-quarters of a revolution?

   • A) $R\sqrt{2}$
   • B) $2R$
   • C) $\frac{3}{2}\pi R$
   • D) $R$
5. 5.

   A particle travels in uniform circular motion along a circular path of radius 0.25 m. If the particle completes 120 revolutions per minute, what is the magnitude of its centripetal acceleration?

   • A) $\pi^2\text{ m/s}^2$
   • B) $2\pi^2\text{ m/s}^2$
   • C) $4\pi^2\text{ m/s}^2$
   • D) $16\pi^2\text{ m/s}^2$
6. 6.

   An object moves in uniform circular motion with a linear speed of 8.0 m/s and a centripetal acceleration of magnitude 40 m/s². What is the angular speed of the object?

   • A) 0.20 rad/s
   • B) 5.0 rad/s
   • C) 1.6 rad/s
   • D) 320 rad/s
7. 7.

   An object moves in uniform circular motion with a constant speed $v$ along a circular path of radius $r$. What are the magnitudes of its tangential acceleration, $a_t$, and its centripetal acceleration, $a_c$?

   • A) $a_t = 0$ and $a_c = \frac{v^2}{r}$
   • B) $a_t = \frac{v^2}{r}$ and $a_c = 0$
   • C) $a_t = \frac{v^2}{r}$ and $a_c = \frac{v^2}{r}$
   • D) $a_t = 0$ and $a_c = 0$
8. 8.

   An object moves in uniform circular motion along a circular path of radius 0.80 m. If the magnitude of its centripetal acceleration is 20 m/s², what is the linear speed of the object?

   • A) 25 m/s
   • B) 16 m/s
   • C) 5.0 m/s
   • D) 4.0 m/s
9. 9.

   A particle moves in uniform circular motion with a constant speed $v$ along a circular track of radius $R$. What is the magnitude of the particle's average acceleration over the time interval required to complete half a revolution?

   • A) 0
   • B) $\frac{v^2}{R}$
   • C) $\frac{2v^2}{\pi R}$
   • D) $\frac{v^2}{\pi R}$
10. 10.

    A wheel rotates in uniform circular motion with a constant angular speed of $8.0\text{ rad/s}$. How many revolutions does the wheel complete in $10\pi\text{ s}$?

    • A) 40
    • B) 80
    • C) 20
    • D) 160
11. 11.

    An object moves in uniform circular motion along a path of radius $R$ with a constant centripetal acceleration of magnitude $a$. Which expression represents the period of the motion?

    • A) $\pi \sqrt{\frac{R}{a}}$
    • B) $2\pi \frac{R}{a}$
    • C) $2\pi \sqrt{\frac{R}{a}}$
    • D) $2\pi \sqrt{\frac{a}{R}}$
12. 12.

    Two carts move in uniform circular motion along concentric circular tracks with the same period. If the radius of cart B's path is three times the radius of cart A's path, what is the ratio of the speed of cart B to the speed of cart A, $v_B / v_A$?

    • A) $\frac{1}{3}$
    • B) $3$
    • C) $\sqrt{3}$
    • D) $9$
13. 13.

    A particle travels in uniform circular motion along a circular path of radius 0.50 m with a constant angular speed of 6.0 rad/s. What distance does the particle cover along the path in 4.0 seconds?

    • A) 3.0 m
    • B) 6.0 m
    • C) 12 m
    • D) 24 m
14. 14.

    An object moves in uniform circular motion along a path of fixed radius. If the period of the motion is doubled, by what factor is the magnitude of the object's centripetal acceleration multiplied?

    • A) $4$
    • B) $2$
    • C) $\frac{1}{2}$
    • D) $\frac{1}{4}$
15. 15.

    Two objects, X and Y, execute uniform circular motion at the same constant speed. If the radius of the path of object X is four times the radius of the path of object Y, what is the ratio of the centripetal acceleration of object X to that of object Y?

    • A) $\frac{1}{4}$
    • B) 1
    • C) 4
    • D) $\frac{1}{16}$
16. 16.

    A particle moves at a constant speed $v$ along a circular path. What is the magnitude of the change in the particle's velocity vector after completing one-quarter of a revolution?

    • A) $0$
    • B) $v$
    • C) $2v$
    • D) $\sqrt{2}v$
17. 17.

    A particle moves with a constant speed $v$ along a circular path of radius $R$. What is the magnitude of the particle's average velocity during the time it takes to travel halfway around the circle?

    • A) $0$
    • B) $\frac{v}{\pi}$
    • C) $v$
    • D) $\frac{2v}{\pi}$
18. 18.

    A runner moves at a constant speed around a circular track of radius 40 m and completes one lap in $16\pi$ seconds. What is the runner's speed?

    • A) 1.25 m/s
    • B) 2.5 m/s
    • C) 5.0 m/s
    • D) 10 m/s
19. 19.

    An object travels at a constant speed along a circular path. Which statement correctly describes the direction of the object's acceleration vector relative to its instantaneous velocity vector?

    • A) The acceleration vector points tangent to the path in the same direction as the velocity vector.
    • B) The acceleration vector is perpendicular to the velocity vector and directed toward the center of the circle.
    • C) The acceleration vector points tangent to the path in the direction opposite to the velocity vector.
    • D) The acceleration vector is perpendicular to the velocity vector and directed radially outward from the center.
20. 20.

    A particle executes uniform circular motion along a circular path of radius $2.0\text{ m}$ at a constant angular speed of $3.0\text{ rad/s}$. What is the magnitude of the centripetal acceleration of the particle?

    • A) $18\text{ m/s}^2$
    • B) $12\text{ m/s}^2$
    • C) $6.0\text{ m/s}^2$
    • D) $4.5\text{ m/s}^2$

Answers and step-by-step solutions appear after you finish the test.