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AP®PhysicsCollege BoardPhysics 1: Algebra-BasedExam QuestionsUnit 2: Force & Translational DynamicsCircular Motion

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

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1
Sme Calculator1 mark

Object X moves around point Y in a circular path with constant frequency.

Which of the following arrows points in the direction of the acceleration of object X?

Object X lies at the top of a dashed circle centered around point Y. Arrow A points vertically upwards, arrow B points horizontally right tangential to the circle, arrow C points diagonally down and right and arrow D points vertically downwards towards point Y.

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    2
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    Two planets orbit the same star. Planet A is 1 AU from the star with an orbital period of 1 year. Planet B is 4 AU from the star. What is the orbital period of Planet B?

    You may use the relation T squared proportional to R cubed.

    • 2 years

    • 4 years

    • 8 years

    • 16 years

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    3
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    A conical pendulum moves in a circular path. The pendulum has mass m while the string has length L, is at an angle theta to the vertical and experiences a tension of magnitude F subscript T.

    Which of the following expressions describes the centripetal force?

    • F subscript T space sin space theta

    • m g space sin space theta

    • F subscript T space cos space theta

    • m g space cos space theta

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    4
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    A racing car is traveling on a circular track. The magnitude of its net acceleration is 12 m/s2 when the driver has pressed on the accelerator pedal for 2.0 s.

    If the centripetal acceleration has a magnitude of 4.0 m/s2, which of the following is most nearly the magnitude of the car's tangential acceleration?

    • 11 m/s2

    • 13 m/s2

    • 16 m/s2

    • 48 m/s2

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    5
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    Which of the following expressions is equal to the period of an object orbiting a body of mass M at distance R in circular motion?

    • fraction numerator 4 straight pi squared over denominator G M end fraction R cubed

    • square root of fraction numerator 2 straight pi over denominator G M end fraction end root R to the power of 1.5 end exponent

    • fraction numerator G M over denominator 4 straight pi squared end fraction R squared

    • fraction numerator 2 straight pi over denominator square root of G M end root end fraction R to the power of 3 over 2 end exponent

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    1
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    A circular diagram showing points A and B on the circumference. Labels: T=1.2s, vA=2m/s, vB=2.25m/s, Δt=0.05s, radius=0.8m with dotted lines connecting points.

    A ball on the end of a string of length 0.8 space straight m is being spun in a horizontal circular path. The instantaneous speed of the ball at point A is 2 space straight m divided by straight s and at point B is 2.25 space straight m divided by straight s. It takes 0.05 space straight s for the ball to pass from point A to point B. It takes 1.2 space straight 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?

    • 5 space straight m divided by straight s squared

    • 9 space straight m divided by straight s squared

    • 16 space straight m divided by straight s squared

    • 20 space straight m divided by straight s squared

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    2
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    Triton is one of Neptune's moons and orbits at a height of 354 comma space 800 space km above the surface of Neptune. It takes 6 Earth days for Triton to complete one orbital rotation of Neptune. Neptune has a mass of 1 space cross times space 10 to the power of 24 space kg.

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

    • 1.8 space cross times space 10 to the power of 5 space straight m

    • 3.2 space cross times space 10 to the power of 7 space straight m

    • 3.6 space cross times space 10 to the power of 8 space straight m

    • 6.8 space cross times space 10 to the power of 8 space straight m

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    3
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    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?

    • fraction numerator 2 straight pi squared T squared over denominator L end fraction

    • fraction numerator 4 straight pi squared L over denominator T squared end fraction

    • fraction numerator 16 straight pi squared L over denominator T squared end fraction

    • fraction numerator 4 straight pi T over denominator L squared end fraction

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    4
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    A car travels at 20 m/s around a banked curve of radius 100 m. The road is frictionless, and the banking angle is ideal.

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

    • 5°

    • 10°

    • 15°

    • 20°

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    5
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    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?

    • Increase the angle of the bank.

    • Increase the mass of the car.

    • Decrease the angle of the bank.

    • Change the material of the tyres.

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    11 mark

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

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

    • v space equals space 2 space straight m divided by straight s

    • v space equals space 4 space straight m divided by straight s

    • v space equals space 7 space straight m divided by straight s

    • v space equals space 36 space straight m divided by straight s

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    2
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    A car of mass 1.4 cross times 10 to the power of 4 space kg is travelling around a banked curve at 76 space km divided by hr. The curve is banked at 4 degree to the horizontal and is rated at a speed of 20 space straight m divided by straight s with a radius of 50 space straight 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?

    • 1.15 cross times 10 to the power of 5 space straight N

    • 1.24 cross times 10 to the power of 5 space straight N

    • 1.26 cross times 10 to the power of 5 space straight N

    • 1.61 cross times 10 to the power of 6 space straight N

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    31 mark

    A ball of mass 0.8 space kg is suspended from the end of a light inextensible string held at an angle of 12 degree to the vertical. The tension in the string is 18 space straight N when the ball moves with uniform horizontal circular motion of radius 26 space cm.

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

    • 0.2 space rad space straight s to the power of negative 1 end exponent

    • 0.7 space rad space straight s to the power of negative 1 end exponent

    • 3.0 space rad space straight s to the power of negative 1 end exponent

    • 6.0 space rad space straight s to the power of negative 1 end exponent

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    4
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    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?

    • 4 straight pi squared f squared d

    • fraction numerator 20 straight pi f over denominator 11 end fraction

    • fraction numerator 40 straight pi squared f squared d over denominator 11 end fraction

    • fraction numerator 40 straight pi squared f squared d over denominator 9 end fraction

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    5
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    A driverless car of mass m space equals space 1500 space kg is being tested on a circular track wirh radius r space equals space 50 space straight m. The track is banked at an angle theta space equals space 20 degree 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 space equals space 19.3 space straight m divided by straight s.

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

    • 0.20

    • 0.30

    • 0.35

    • 0.40

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