Centripetal acceleration Transitional Reasoning Practice

Questions

1. 1.

   A robotic delivery rover navigates a flat circular bend at a constant speed. Telemetry data shows that the rover traverses a circular arc of 48 m in 4.0 s while its direction of travel rotates through an angle of 0.80 rad. What is the magnitude of the centripetal acceleration experienced by the rover during this turn?

   • A) 1.2 m/s²
   • B) 2.4 m/s²
   • C) 4.8 m/s²
   • D) 9.6 m/s²
2. 2.

   To evaluate structural fatigue on a wind turbine, an instrumentation sensor is attached to the tip of a rotor blade of length $R$. When the turbine operates at a steady rotational frequency $f$, the sensor detects a centripetal acceleration of magnitude $a$. In an upgraded configuration, the turbine is fitted with blades of length $1.25R$ and operates at an increased rotational frequency of $1.2f$. In terms of $a$, what is the magnitude of the centripetal acceleration detected by the sensor in the upgraded configuration?

   • A) $1.44a$
   • B) $1.50a$
   • C) $2.25a$
   • D) $1.80a$
3. 3.

   A flight-simulation capsule mounted on a rotating mechanical arm undergoes uniform circular motion, experiencing a centripetal acceleration of magnitude $a$ when operating with period $T$ and tangential speed $v$. For an advanced simulation run, the control system reduces the period of rotation to $0.5T$ and simultaneously adjusts the capsule's position along the arm so that its tangential speed becomes $1.5v$. What is the magnitude of the centripetal acceleration experienced by the capsule during this advanced simulation run?

   • A) $2.25a$
   • B) $3.0a$
   • C) $4.5a$
   • D) $6.0a$
4. 4.

   During quality-control testing, an aerospace component is secured to a horizontal centrifuge arm rotating at a constant angular speed of $4.0\text{ rad/s}$. The component is initially mounted at a radial distance of 0.50 m from the central axis of rotation and is subsequently repositioned to a radial distance of 1.25 m on the same arm. By how much does the magnitude of the centripetal acceleration experienced by the component increase following this repositioning?

   • A) 12.0 m/s²
   • B) 20.0 m/s²
   • C) 8.0 m/s²
   • D) 3.0 m/s²
5. 5.

   An autonomous inspection drone maneuvers along a flat circular arc of radius 16 m while maintaining a constant centripetal acceleration of magnitude 4.0 m/s². The guidance system navigates the drone through a continuous quarter-circle turn along this path. How much time does the drone take to complete this turn?

   • A) $\pi$ s
   • B) $2\pi$ s
   • C) $\frac{\pi}{2}$ s
   • D) $4\pi$ s
6. 6.

   In an industrial robotics mechanism, two interlocking spur gears, Gear X and Gear Y, rotate smoothly without slipping at their point of contact. The pitch radius of Gear X is 15 cm, and the pitch radius of Gear Y is 5 cm. While the mechanism operates at a constant operational speed, a point on the perimeter of Gear X experiences a centripetal acceleration of magnitude $a$. What is the magnitude of the centripetal acceleration experienced by a point on the perimeter of Gear Y?

   • A) $\frac{1}{3}a$
   • B) $a$
   • C) $3a$
   • D) $9a$
7. 7.

   Transportation engineers evaluate passenger comfort on a high-speed railway by monitoring lateral acceleration along two consecutive circular curves, Curve 1 and Curve 2. The train enters Curve 1 at speed $v$ and later navigates Curve 2 at an increased speed of $1.5v$. To maintain passenger comfort, Curve 2 is designed such that the centripetal acceleration experienced on Curve 2 is exactly half of that on Curve 1. Based on this design requirement, what is the ratio of the radius of curvature of Curve 2 to that of Curve 1 ($R_2 / R_1$)?

   • A) $\frac{3}{4}$
   • B) $\frac{9}{4}$
   • C) $\frac{9}{2}$
   • D) $\frac{3}{1}$
8. 8.

   A civil engineering team is calibrating the speed profile of an autonomous vehicle navigating curved highway ramps. On Ramp X, which has a radius of curvature of 80 m, the vehicle travels at a constant speed of 20 m/s. The vehicle then transitions onto Ramp Y, which has a wider radius of curvature of 180 m. If the vehicle is programmed to experience the exact same magnitude of centripetal acceleration on both ramps, what constant speed must it maintain along Ramp Y?

   • A) 15 m/s
   • B) 30 m/s
   • C) 45 m/s
   • D) 60 m/s
9. 9.

   During a performance test on a flat proving ground, an electric vehicle travels at a constant speed $v$ along a circular bend of radius $R$, producing a centripetal acceleration of magnitude $a$. On the next section of the track, the vehicle enters a sharper bend with a radius of curvature of $\frac{1}{2}R$ while maintaining an increased constant speed of $2v$. In terms of $a$, what is the magnitude of the centripetal acceleration experienced by the vehicle on the sharper bend?

   • A) $2a$
   • B) $4a$
   • C) $16a$
   • D) $8a$
10. 10.

    A robotic test vehicle travels at a constant speed along a horizontal circular track of radius $R$, experiencing a centripetal acceleration of magnitude $a$. In a subsequent trial, the vehicle navigates a wider concentric circular track of radius $3R$ such that it completes one full lap in the same period of time as in the first trial. Based on this information, what is the magnitude of the vehicle's centripetal acceleration during the second trial?

    • A) $3a$
    • B) $9a$
    • C) $a$
    • D) $\frac{a}{3}$

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