Centripetal acceleration Knowledge-Based Download PDF

Questions

1. 1.

   A particle moves along a circular path with a tangential speed of 8.0 m/s and an angular speed of 4.0 rad/s. What is the magnitude of the particle's centripetal acceleration?

   • A) 32 m/s$^2$
   • B) 16 m/s$^2$
   • C) 2.0 m/s$^2$
   • D) 64 m/s$^2$
2. 2.

   Car A travels at a constant speed of 12 m/s around a circular bend with a radius of 36 m. Car B experiences the exact same magnitude of centripetal acceleration while navigating a circular bend with a radius of 144 m. What is the speed of Car B?

   • A) 6.0 m/s
   • B) 18 m/s
   • C) 24 m/s
   • D) 48 m/s
3. 3.

   A small sphere moves along a horizontal circular path of radius 0.40 m at a constant angular speed of 5.0 rad/s. What is the magnitude of the sphere's centripetal acceleration?

   • A) 10 m/s²
   • B) 2.0 m/s²
   • C) 12.5 m/s²
   • D) 62.5 m/s²
4. 4.

   An object moves in uniform circular motion at a constant speed. Why does the object experience a non-zero centripetal acceleration?

   • A) The direction of its velocity vector changes continuously.
   • B) The magnitude of its velocity vector increases continuously.
   • C) A net force acts parallel to its instantaneous velocity.
   • D) Its total displacement increases continuously over each completed revolution.
5. 5.

   An object moves at a constant speed along a circular path in a horizontal plane. Which statement correctly describes the object's centripetal acceleration vector?

   • A) Its magnitude remains constant, but its direction continuously changes.
   • B) Both its magnitude and its direction remain constant.
   • C) Its magnitude continuously changes, but its direction remains constant.
   • D) Both its magnitude and its direction continuously change.
6. 6.

   Two small blocks rest on a flat turntable rotating at a constant angular speed. If Block 1 is at a distance $r$ from the rotation axis and Block 2 is at a distance $2r$, what is the ratio of the magnitude of the centripetal acceleration of Block 1 to that of Block 2?

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

   A small probe moves in a uniform circular orbit of radius $r$ with an orbital period $T$. Which expression represents the magnitude of the probe's centripetal acceleration in terms of $r$ and $T$?

   • A) $\frac{2\pi r}{T^2}$
   • B) $\frac{4\pi^2 r}{T^2}$
   • C) $\frac{4\pi^2 r^2}{T}$
   • D) $\frac{2\pi r^2}{T}$
8. 8.

   A particle moves in uniform circular motion with speed $v$ along a path of radius $r$. If the speed is doubled while the radius of the path is quadrupled, how does the magnitude of the particle's centripetal acceleration change?

   • A) It increases by a factor of 8.
   • B) It increases by a factor of 2.
   • C) It decreases to half its original value.
   • D) It remains unchanged.
9. 9.

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

   • A) The velocity vector is tangent to the path, while the centripetal acceleration vector points toward the center of the circle.
   • B) The velocity vector points toward the center of the circle, while the centripetal acceleration vector is tangent to the path.
   • C) Both the velocity vector and the centripetal acceleration vector point directly toward the center of the circle.
   • D) Both the velocity vector and the centripetal acceleration vector are directed tangent to the path in the direction of motion.
10. 10.

    A vehicle moves at a constant speed of 20 m/s along a circular track with a radius of 80 m. What is the magnitude of the vehicle's centripetal acceleration?

    • A) $5.0\text{ m/s}^2$
    • B) $0.25\text{ m/s}^2$
    • C) $4.0\text{ m/s}^2$
    • D) $0\text{ m/s}^2$