Uniform circular motion (kinematics) Knowledge-Based Download PDF

Questions

1. 1.

   Two cars, A and B, travel at constant speeds around the same circular track. If Car A completes one lap in 40 s and Car B completes one lap in 60 s, what is the ratio of the angular speed of Car A to that of Car B?

   • A) 4/9
   • B) 2/3
   • C) 3/2
   • D) 9/4
2. 2.

   A particle executes uniform circular motion at a constant frequency of 5.0 Hz. What is the total angle swept out by the particle's position vector in 4.0 s?

   • A) $2.5\pi$ rad
   • B) $10\pi$ rad
   • C) $20\pi$ rad
   • D) $40\pi$ rad
3. 3.

   What is the angle between the instantaneous velocity vector and the instantaneous acceleration vector of a particle executing uniform circular motion?

   • A) $90^\circ$
   • B) $0^\circ$
   • C) $45^\circ$
   • D) $180^\circ$
4. 4.

   A particle executes uniform circular motion with a constant linear speed $v$ and an angular speed $\omega$. Which expression represents the magnitude of the particle's centripetal acceleration?

   • A) $v\omega$
   • B) $\frac{v}{\omega}$
   • C) $\frac{v^2}{\omega}$
   • D) $\frac{\omega^2}{v}$
5. 5.

   An object undergoes uniform circular motion along a circular path of radius 25 m with a centripetal acceleration of 4.0 m/s². What is the speed of the object?

   • A) 0.16 m/s
   • B) 6.25 m/s
   • C) 10 m/s
   • D) 100 m/s
6. 6.

   A particle moves along a circular path of radius $r$ at a constant speed $v$. What is the magnitude of the particle's angular acceleration?

   • A) $v^2 / r$
   • B) 0
   • C) $v / r$
   • D) $v^2 / r^2$
7. 7.

   A particle executes uniform circular motion with a constant angular speed $\omega$ in a path centered at the origin. If $\vec{r}$ is the instantaneous position vector of the particle relative to the origin, which expression represents its instantaneous acceleration vector $\vec{a}$?

   • A) $\vec{a} = \omega^2 \vec{r}$
   • B) $\vec{a} = \omega \vec{r}$
   • C) $\vec{a} = -\omega^2 \vec{r}$
   • D) $\vec{a} = -\omega \vec{r}$
8. 8.

   An object moves along a circular path of radius 3.0 m at a constant speed. If the object sweeps out a central angle of 1.5 rad in a time interval of 0.50 s, what is its linear speed?

   • A) 1.0 m/s
   • B) 3.0 m/s
   • C) 9.0 m/s
   • D) 13.5 m/s
9. 9.

   A particle moves at a constant speed $v$ along a circular path of radius $R$. What is the time required for the direction of the particle's velocity vector to rotate by $90^\circ$?

   • A) $\frac{2\pi R}{v}$
   • B) $\frac{\pi R}{v}$
   • C) $\frac{\pi R}{2v}$
   • D) $\frac{\pi R}{4v}$
10. 10.

    A particle moves along a circular path of radius 2.0 m at a constant speed, taking 4.0 s to complete one full revolution. What total distance does the particle travel in 12 s?

    • A) $4\pi$ m
    • B) $6\pi$ m
    • C) $12\pi$ m
    • D) $24\pi$ m
11. 11.

    Two particles, A and B, execute uniform circular motion with the same period. The radius of the circular path of particle A is $r$, while the radius of the circular path of particle B is $3r$. What is the ratio of the magnitude of the centripetal acceleration of particle A to that of particle B?

    • A) 1/3
    • B) 3
    • C) 1/9
    • D) 9
12. 12.

    A particle undergoes uniform circular motion along a circular path of radius $R$. What is the magnitude of the displacement of the particle after it sweeps through a central angle of $120^\circ$?

    • A) $R\sqrt{3}$
    • B) $R\sqrt{2}$
    • C) $R$
    • D) $\frac{2\pi R}{3}$
13. 13.

    An object moves along a circular path of radius $r$ at a constant speed $v$. What is the magnitude of its average acceleration over a time interval during which it completes one-half of a revolution?

    • A) 0
    • B) $\frac{v^2}{r}$
    • C) $\frac{v^2}{\pi r}$
    • D) $\frac{2v^2}{\pi r}$
14. 14.

    A particle executes uniform circular motion along a circular path of radius $R$ with a constant centripetal acceleration of magnitude $a$. Which expression represents the time required for the particle to complete one full revolution?

    • A) $2\pi \sqrt{\frac{a}{R}}$
    • B) $2\pi \frac{R}{a}$
    • C) $\pi \sqrt{\frac{R}{a}}$
    • D) $2\pi \sqrt{\frac{R}{a}}$
15. 15.

    Which statement correctly describes the tangential acceleration and centripetal acceleration of an object undergoing uniform circular motion?

    • A) Tangential acceleration is non-zero, while centripetal acceleration is zero.
    • B) Both tangential acceleration and centripetal acceleration are non-zero.
    • C) Tangential acceleration is zero, while centripetal acceleration is non-zero.
    • D) Both tangential acceleration and centripetal acceleration are zero.
16. 16.

    A particle undergoes uniform circular motion with angular speed $\omega$ along a circular path of radius $R$. If the angular speed is doubled while the radius is reduced to one-fourth of its initial value, what happens to the magnitude of the particle's centripetal acceleration?

    • A) It remains unchanged.
    • B) It doubles.
    • C) It quadruples.
    • D) It is halved.
17. 17.

    An object moves at a constant speed of 10 m/s around a circular track. What is the magnitude of the change in the object's velocity vector after it completes one-quarter of a revolution?

    • A) 0 m/s
    • B) 10 m/s
    • C) 20 m/s
    • D) $10\sqrt{2}$ m/s
18. 18.

    A particle travels at a constant speed along a circular track of radius 5.0 m with a period of 10 s. What is the magnitude of the particle's average velocity over any half-revolution interval?

    • A) 0 m/s
    • B) 1.0 m/s
    • C) 2.0 m/s
    • D) 3.1 m/s
19. 19.

    A particle travels at a constant speed in a horizontal circular path of radius $0.50\text{ m}$, completing $3.0$ revolutions every second. What is the magnitude of the particle's centripetal acceleration?

    • A) $4.5\pi^2\text{ m/s}^2$
    • B) $6.0\pi^2\text{ m/s}^2$
    • C) $9.0\pi^2\text{ m/s}^2$
    • D) $18\pi^2\text{ m/s}^2$