Centripetal acceleration Transitional Reasoning Download PDF

Questions

1. 1.

   A high-speed train travels along a horizontal circular curve at a constant speed of 40 m/s. An onboard inertial guidance system records that the train's heading changes uniformly by 0.50 rad over an elapsed travel time of 5.0 s. What is the magnitude of the train's centripetal acceleration while navigating this curve?

   • A) 4.0 m/s$^2$
   • B) 8.0 m/s$^2$
   • C) 2.0 m/s$^2$
   • D) 20 m/s$^2$
2. 2.

   A civil engineer evaluates the safety profile of a curved bypass road designed as a horizontal circular arc with a radius of 125 m. To guarantee passenger comfort and vehicle stability, transportation regulations specify that a vehicle navigating this curve must experience a centripetal acceleration no greater than 3.2 m/s2. Based on this threshold, what is the maximum recommended speed limit that should be posted for this curve, expressed in kilometers per hour (km/h)?

   • A) 72 km/h
   • B) 54 km/h
   • C) 36 km/h
   • D) 20 km/h
3. 3.

   In an amusement park rotor ride, passengers stand against the inner vertical wall of a cylindrical drum with a radius of 4.0 m. When the ride operates at its target speed, a passenger on the wall experiences a constant centripetal acceleration of 16 m/s$^2$. Taking $\pi \approx 3$, how many complete revolutions does the drum make in one minute to maintain this centripetal acceleration?

   • A) 20
   • B) 40
   • C) 80
   • D) 10
4. 4.

   A passenger monorail travels at a constant speed along a horizontal curve designed as a quarter-circle arc of length 314 m. An onboard monitoring system records that the monorail takes exactly 15.7 s to traverse this curved section from start to finish. Taking $\pi \approx 3.14$, what is the magnitude of the monorail's centripetal acceleration along this curve?

   • A) 8.0 m/s$^2$
   • B) 1.3 m/s$^2$
   • C) 4.0 m/s$^2$
   • D) 2.0 m/s$^2$
5. 5.

   An autonomous delivery vehicle traverses a proving ground containing two circular curved sections, Track 1 and Track 2, with radii of curvature of 40 m and 90 m, respectively. To prevent delicate onboard sensors from shifting, the vehicle's control system is programmed so that its centripetal acceleration does not exceed the same threshold limit along either curve. If the vehicle navigates Track 1 at its maximum allowable speed of 12 m/s, what is its maximum allowable speed along Track 2?

   • A) 8 m/s
   • B) 18 m/s
   • C) 27 m/s
   • D) 36 m/s
6. 6.

   A transit engineer measures the lateral dynamics of an electric bus traveling along a flat circular bend on a test track. During an initial trial, the bus navigates the bend at a constant speed of 20 m/s, resulting in a centripetal acceleration of 2.0 m/s$^2$. If the bus rounds the exact same curve at a constant speed of 30 m/s during a high-speed trial, what is the magnitude of its centripetal acceleration?

   • A) 3.0 m/s$^2$
   • B) 4.0 m/s$^2$
   • C) 4.5 m/s$^2$
   • D) 6.0 m/s$^2$
7. 7.

   An aerospace technician tests two small probe modules, Alpha and Beta, in a high-speed centrifuge. Module Alpha is positioned at a distance $r$ from the central axis and completes one full revolution every $T$ seconds. Module Beta is positioned at a distance $3r$ from the axis and completes one full revolution every $2T$ seconds. What is the ratio of the magnitude of the centripetal acceleration experienced by Module Beta to that experienced by Module Alpha, $\frac{a_{\text{Beta}}}{a_{\text{Alpha}}}$?

   • A) $\frac{3}{2}$
   • B) $\frac{4}{3}$
   • C) $\frac{9}{4}$
   • D) $\frac{3}{4}$
8. 8.

   An automated inspection drone travels counterclockwise at a constant speed along a horizontal circular track centered at a central ground station. When the drone passes the northernmost point of the track, its onboard sensor records a centripetal acceleration of magnitude $a$ directed due south toward the station. When the drone reaches the easternmost point of the track while maintaining the same speed, what are the magnitude and direction of its centripetal acceleration?

   • A) Magnitude 0, with no defined direction
   • B) Magnitude $a$, directed due north
   • C) Magnitude $a$, directed due west
   • D) Magnitude $a$, directed due south
9. 9.

   A wind turbine blade rotates horizontally about a fixed central pivot at a constant angular speed. Two diagnostic sensors, P and Q, are fixed along the blade at radial distances of 12 m and 36 m from the pivot, respectively. How does the magnitude of the centripetal acceleration of sensor Q compare to that of sensor P?

   • A) The centripetal acceleration of Q is one-third that of P, because centripetal acceleration is inversely proportional to the radius.
   • B) The centripetal acceleration of Q is three times that of P, because both sensors have the same angular speed and acceleration is directly proportional to radius.
   • C) The centripetal acceleration of Q is nine times that of P, because centripetal acceleration depends on the square of the radius.
   • D) The centripetal acceleration of Q is equal to that of P, because all fixed points on the same rigid blade share an identical acceleration.
10. 10.

    During a safety performance test, two robotic carts travel at constant speeds along concentric circular tracks on a horizontal test surface. Cart X follows an inner track of radius $R$ at a constant speed of $v$, while Cart Y follows an outer track of radius $2R$ at a constant speed of $2v$. Based on their trajectories, how does the magnitude of the centripetal acceleration of Cart Y compare to that of Cart X?

    • A) It is half as large.
    • B) It is twice as large.
    • C) It is equal in magnitude.
    • D) It is four times as large.