Circular Motion (College Board AP® Physics 1: Algebra-Based): Exam Questions

A ball on the end of a string of length $0.8\mathrm{m}$ is being spun in a horizontal circular path. The instantaneous speed of the ball at point A is $2\mathrm{m}/\mathrm{s}$ and at point B is $2.25\mathrm{m}/\mathrm{s}$. It takes $0.05\mathrm{s}$ for the ball to pass from point A to point B. It takes $1.2\mathrm{s}$ for the ball to make one full rotation of the circular path.

Which of the following is most nearly the magnitude of the net acceleration of the ball between points A and B?

Triton is one of Neptune's moons and orbits at a distance of $330000\mathrm{km}$ above the surface of Neptune. It takes approximately 6 Earth days for Triton to complete one orbit of Neptune. Neptune has a mass of $1.0\times {10}^{26}\mathrm{kg}$.

Which of the following is the best estimate for the radius of Neptune?

A planet orbits a star in a circular path with period $T$. The planet is a distance $L$ from the star.

Which of the following is the correct expression for the planet's acceleration?

A car travels at $20\mathrm{m}/\mathrm{s}$ around a banked curve of radius $100\mathrm{m}$. The road is frictionless, and the banking angle is ideal.

Which of the following is most nearly the angle of the banked curve?

A car drives in circular motion on a frictionless banked surface at the ideal speed for the bank's incline. On a second lap, the driver presses down harder on the gas pedal.

Which of the following changes would need to be made to ensure the car follows the initial path of circular motion?

A yo-yo of mass $500\mathrm{g}$ is rotated in a vertical circular path on the end of a string $50\mathrm{cm}$ long. At the lowest point in the path the tension in the string is $20\mathrm{N}$.

Which of the following is most nearly the tangential speed of the bucket?

A car of mass $1.4\times {10}^4\mathrm{kg}$ is travelling around a banked curve at $76\mathrm{km}/\mathrm{hr}$. The curve is banked at $4°$ to the horizontal and is rated at a speed of $20\mathrm{m}/\mathrm{s}$ with a radius of $50\mathrm{m}$.

Which of the following is the closest estimate of the sideways frictional force required between the car and the road to keep the car in its lane as it drives around the curve?

A ball of mass $0.8\mathrm{kg}$ is suspended from the end of a light, inextensible string and held at an angle $12°$ with the vertical. The ball is made to move with uniform horizontal circular motion of radius $26\mathrm{cm}$.

Which of the following is most nearly the angular velocity of the ball?

A string of length $d$ is tied to the handle of a bucket. A science teacher holds the end of the string and swings the bucket around in a vertical circle with frequency $f$.

Inside the bucket is a metal block of mass. At the top of the circle, the block exerts a force of on the base of the bucket equal in magnitude to one tenth of the block's weight.

Which of the following expressions is equal to the acceleration due to gravity?

A driverless car of mass $m=1500\mathrm{kg}$ is being tested on a circular track wirh radius $r=50\mathrm{m}$. The track is banked at an angle $\theta =20°$ and the car is above ideal speed.

The car's linear speed continues to increase until it slides out of its circular path. At the instant before it leaves circular motion, the car's linear speed is $v=19.3\mathrm{m}/\mathrm{s}$.

Which of the following is most nearly the coefficient of static friction between the car's tyres and the track?