Centripetal acceleration Knowledge-Based Practice

Questions

1. 1.

   An object moves in a circular path of radius $r$ with a constant centripetal acceleration of magnitude $a$. Which expression correctly gives the period of revolution $T$ of the object?

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

   A particle moves in a circular path with linear speed $v$ and angular speed $\omega$. Which expression correctly gives the magnitude of the particle's centripetal acceleration?

   • A) $\frac{v}{\omega}$
   • B) $\frac{v^2}{\omega}$
   • C) $v\omega$
   • D) $v\omega^2$
3. 3.

   An object moves at a constant speed along a horizontal circular path. Which statement correctly describes the magnitude and direction of the object's centripetal acceleration during this motion?

   • A) Both the magnitude and the direction remain constant.
   • B) The magnitude remains constant, but the direction continuously changes.
   • C) The magnitude continuously changes, but the direction remains constant.
   • D) Both the magnitude and the direction continuously change.
4. 4.

   Two cars travel around separate circular tracks at constant speeds. If Car A moves along a track of radius $R$ at speed $v$, and Car B moves along a track of radius $4R$ with the same centripetal acceleration as Car A, what is the speed of Car B?

   • A) $\frac{1}{2}v$
   • B) $2v$
   • C) $4v$
   • D) $16v$
5. 5.

   An object moves at a constant speed along a circular path. Which statement correctly explains why the object experiences a centripetal acceleration?

   • A) Its instantaneous speed continuously increases and decreases along the tangent to the curve.
   • B) Its net displacement over one complete revolution is zero, which requires an internal acceleration.
   • C) An outward force continuously acts on the object to alter the magnitude of its momentum.
   • D) The direction of its velocity vector is continuously changing, producing a rate of change of velocity directed toward the center of the path.
6. 6.

   A flat disk rotates about a fixed central axis at a constant angular speed. If Point 1 is located at a distance $r$ from the axis and Point 2 is located at a distance $2r$ from the axis, what is the ratio of the magnitude of the centripetal acceleration of Point 2 to that of Point 1?

   • A) 1/4
   • B) 1/2
   • C) 2
   • D) 4
7. 7.

   A bicyclist travels along a circular path of radius 25 m at a constant speed of 10 m/s. What is the magnitude of the bicyclist's centripetal acceleration?

   • A) $4.0\text{ m/s}^2$
   • B) $0.40\text{ m/s}^2$
   • C) $2.5\text{ m/s}^2$
   • D) $8.0\text{ m/s}^2$
8. 8.

   An object moves at a constant speed along a horizontal circular path. Which statement correctly describes the directions of the object's velocity and acceleration vectors at any given instant?

   • A) The velocity and acceleration vectors both point tangent to the circular path in the direction of motion.
   • B) The velocity vector points toward the center of the circular path, while the acceleration vector points tangent to the path.
   • C) The velocity vector points tangent to the path, while the acceleration vector points radially outward away from the center.
   • D) The velocity vector points tangent to the circular path, while the acceleration vector points radially inward toward the center.
9. 9.

   A particle moves in a circular path of constant radius $r$ at a constant speed, completing one revolution in period $T$. If the period of revolution is doubled while the radius of the path remains unchanged, how does the magnitude of the particle's centripetal acceleration change?

   • A) It increases to four times its original value.
   • B) It increases to twice its original value.
   • C) It decreases to half of its original value.
   • D) It decreases to one-fourth of its original value.
10. 10.

    An object travels at a constant speed $v$ along a circular track of radius $r$ with a centripetal acceleration of magnitude $a$. If the speed of the object is doubled and the radius of the track is halved, what is the new magnitude of its centripetal acceleration in terms of $a$?

    • A) $8a$
    • B) $4a$
    • C) $2a$
    • D) $\frac{a}{2}$

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