Circular Motion - AP Physics 1

A satellite moves at constant speed in a circular orbit around Earth. Ignoring air resistance, what is the direction of the satellite's net force at any instant?
Answer: Toward Earth's center (radially inward) This question tests understanding of orbital motion and centripetal force. A satellite in circular orbit experiences only Earth's gravitational force, which points toward Earth's center (C), providing the centripetal acceleration needed for circular motion. This inward force continuously changes the satellite's velocity direction without changing its speed, maintaining the circular orbit. The force cannot be tangential (A) as this would change the orbital speed, and there's no outward force due to inertia (B) - inertia simply means the satellite would move in a straight line if no force acted on it. The key insight is that gravity serves as the centripetal force in orbital motion, always pointing toward the center of the orbit.
A 0.40 kg mass moves at constant speed in a circle on a string. At some instant, the tension force on the mass points toward the center. Which statement about the mass's acceleration is correct?
Answer: It points toward the center because the net force is inward This question assesses understanding of acceleration in uniform circular motion. In uniform circular motion, the centripetal acceleration always points toward the center of the circle, changing the direction of the velocity while keeping the speed constant. The net force, according to Newton's second law, must also point toward the center to provide this acceleration. With tension toward the center, the acceleration points inward toward the center. Choice D is incorrect because there is no outward centrifugal force; acceleration follows the net force inward. To relate force and acceleration in circular motion, apply F_net = ma_c, where $a_c$ is v²/r toward the center.
A student swings a rubber stopper in a horizontal circle at constant speed. The string breaks when the stopper is at the south point of the circle. Immediately after the break, which direction does the stopper initially travel?
Answer: Along the tangent to the circle at that point This question assesses understanding of motion after loss of centripetal force in circular motion. In uniform circular motion, the centripetal acceleration always points toward the center of the circle, changing the direction of the velocity while keeping the speed constant. The net force, according to Newton's second law, must also point toward the center to provide this acceleration. When the string breaks, the net force vanishes, and by Newton's first law, the stopper moves tangent to the circle. Choice B is incorrect because there is no outward force; the motion becomes linear tangent to the path. To predict motion after force removal, apply the principle of inertia and continue with the instantaneous velocity vector.
A 1.0 kg mass moves in a vertical circle at constant speed, attached to a light string. At the top of the circle, what is the direction of the mass's acceleration?
Answer: Downward, toward the center of the circle This question examines acceleration direction in vertical circular motion. At any point in circular motion at constant speed, acceleration points toward the center of the circle. At the top of a vertical circle, "toward the center" means downward. Both gravity and string tension act downward at this point, providing the required centripetal force. Choice B incorrectly assumes the string must pull upward at the top, but tension can act in any direction along the string. For vertical circular motion, always identify the center first, then recognize that acceleration points toward it regardless of the object's position on the circle.
A satellite orbits Earth in a nearly circular path at constant speed. Neglecting air resistance, which statement best describes the net force on the satellite?
Answer: It points toward Earth's center due to gravity This question tests understanding of orbital motion as circular motion. A satellite in circular orbit experiences centripetal acceleration toward Earth's center, requiring a net force in the same direction. This force is provided by Earth's gravity, which always points toward Earth's center. Even though the satellite's speed is constant, its velocity direction continuously changes, requiring this inward force. Choice D incorrectly mentions "centrifugal force," which is not a real force but a fictitious effect in rotating reference frames. The strategy is to recognize that orbital motion is circular motion where gravity provides the centripetal force, always pointing toward the central body.
A puck moves at constant speed in a circle on a horizontal air table, attached by a string to a central post. If the string suddenly breaks, which statement best describes the puck's immediate acceleration right after the break?
Answer: It has approximately zero acceleration and moves in a straight line tangent to the circle This question tests understanding of motion when centripetal force is removed. When the string breaks, the centripetal force disappears, so the puck has approximately zero acceleration and continues moving in a straight line tangent to the circle (B). This follows Newton's first law - without a net force, the puck maintains its velocity at the instant of release, which was tangent to the circle. The puck doesn't accelerate outward (A) because there's no force pushing it outward, and it doesn't accelerate toward the center (C) because the string tension that provided centripetal force is gone. The strategy is to apply Newton's first law: when forces become zero, objects maintain their instantaneous velocity.
A satellite moves in a circular orbit around Earth at constant speed. Ignoring air resistance and thrust, what is the direction of the satellite's net force?
Answer: Radially inward, toward Earth's center This question tests understanding of orbital motion as circular motion. A satellite in circular orbit requires centripetal acceleration directed toward Earth's center to maintain its curved path. By Newton's second law, the net force must point in the same direction—radially inward toward Earth. This force is gravity, which always points toward Earth's center. Choice C incorrectly assumes that constant speed means zero acceleration, ignoring that velocity direction changes continuously in circular motion. When analyzing orbital motion, recognize it as circular motion where gravity provides the required centripetal force directed toward the central body.
A small cart moves at constant speed along a circular track on a horizontal table. At the leftmost point of the circle, the cart is moving downward. What is the direction of the cart's acceleration at that instant?
Answer: To the right, toward the center of the circle This question assesses understanding of acceleration direction in uniform circular motion on a track. Centripetal acceleration always points toward the center, independent of the velocity's direction at any instant. This inward acceleration results from a net force that curves the path. At the leftmost point, with the center to the right, acceleration is rightward. Choice D is a distractor suggesting a leftward centrifugal force, but centrifugal force is not real in inertial frames. To find acceleration direction, visualize the circle's center and direct the vector inward from the object's position.
A 0.50 kg ball on a string moves in a vertical circle of radius 1.2 m at constant speed. At the very bottom of the circle, the ball's speed is 4.0 m/s. Which direction is the ball's centripetal acceleration at that instant?
Answer: Upward, toward the center of the circle This question assesses understanding of centripetal acceleration in vertical circular motion. Even in a vertical circle, the centripetal acceleration points toward the center, required for the curved path. The net force causing this acceleration varies with position due to gravity, but the acceleration direction remains inward. At the bottom, the center is upward, so acceleration is upward. Choice D is a distractor implying an outward direction, which might stem from misunderstanding inertia or fictitious forces. When solving for acceleration direction in circular motion, consistently direct it toward the center, adjusting for any additional forces like gravity in calculations.
A student swings a yo-yo on a string in a horizontal circle at constant speed. The yo-yo is momentarily at the point farthest east. Which statement about the net force on the yo-yo is correct?
Answer: It points toward the center of the circle (westward) This question assesses understanding of net force in horizontal circular motion with a string. The net force is centripetal, pointing toward the center to cause inward acceleration. Tension provides this force, pulling the yo-yo inward. At the easternmost point, the center is westward, so net force is westward. Choice D is a distractor claiming an outward centrifugal force, which is incorrect in the inertial frame. A useful strategy is to ignore fictitious forces and always direct the net force toward the center in circular motion analyses.
A 0.20 kg ball is tied to a string and whirled in a horizontal circle of radius 0.80 m at constant speed. The ball completes one revolution every 1.6 s while the string stays taut. Which statement best describes the direction of the ball's acceleration at an instant during the motion?
Answer: Radially inward, toward the center of the circle This question tests understanding of acceleration direction in circular motion. When an object moves in a circle at constant speed, it experiences centripetal acceleration that always points toward the center of the circle, making the answer radially inward (A). Even though the speed is constant, the velocity vector is constantly changing direction, requiring an acceleration perpendicular to the velocity. The ball's acceleration cannot be tangential (B) because that would change the speed, and there is no such thing as centrifugal force (C) in an inertial reference frame. A key strategy is to remember that circular motion always requires center-pointing acceleration to continuously change the direction of velocity.
A satellite travels at constant speed in a circular orbit around Earth. At a particular point in its orbit, what is the direction of the satellite's acceleration?
Answer: Toward Earth's center This question assesses understanding of acceleration in orbital circular motion. In uniform circular motion, acceleration is centripetal, directed toward the center of the orbit. For a satellite, gravity provides this inward force, pointing toward Earth's center. This keeps the satellite in orbit at constant speed. Choice C is a distractor mentioning centrifugal force outward, but that's a fictitious force not applicable here. To solve similar problems, recall that acceleration in circular orbits always points to the central body, aiding in analyzing gravitational forces.
A 0.10 kg mass moves in a horizontal circle of radius 0.40 m at constant speed 2.0 m/s. At one instant the mass is at the bottom of the circle (southmost point). Which direction is the net force on the mass?
Answer: Toward the center of the circle (northward) This question assesses understanding of net force direction in horizontal uniform circular motion. The net force provides centripetal acceleration toward the center, maintaining the circular path. This force is inward, countering the tendency to move in a straight line. At the southmost point, the center is northward, so net force points north. Choice B is a distractor implying an outward force, which might confuse centripetal with centrifugal concepts. Always remember that in circular motion problems, the net force direction is toward the center, helping to identify it regardless of the setup.
A cyclist rides at constant speed around a flat circular path. The only horizontal force on the cyclist-bike system is static friction from the ground. What is the direction of that friction force?
Answer: Radially inward, toward the center of the circle This question tests understanding of friction's role in providing centripetal force. For the cyclist to maintain circular motion at constant speed, a net force must point toward the center of the circle. On a flat path, this centripetal force comes from static friction between the tires and ground, which must point radially inward. Without this inward friction force, the cyclist would continue in a straight line tangent to the circle. Choice B represents the common misconception of an outward "centrifugal force," which doesn't exist in an inertial reference frame. When analyzing circular motion on surfaces, identify friction as the force that prevents sliding outward and provides the required inward acceleration.
A skater glides at constant speed in a circle on level ice, held by a horizontal rope attached to a post at the center. At a given instant, which force provides the inward (centripetal) net force on the skater?
Answer: The rope's tension pulling toward the post This question assesses understanding of the source of centripetal force in uniform circular motion. Centripetal acceleration toward the center is provided by a net force in that direction, such as tension in this case. The tension in the rope pulls inward, serving as the centripetal force to keep the skater circling. No outward forces act; the motion is maintained by this inward net force. Choice A is a distractor attributing the force to inertia pulling outward, which confuses the tendency to move tangentially with an actual force. For identifying centripetal forces, examine real forces acting on the object and determine which provides the inward component.
A 0.10 kg mass moves at constant speed in a horizontal circle of radius 0.80 m on a string. The string provides the only horizontal force on the mass. What is the direction of the tension force on the mass?
Answer: Radially inward, toward the center This question tests understanding of force direction in horizontal circular motion. For the mass to move in a circle at constant speed, it needs a centripetal force pointing toward the center. The string provides this force through tension, which must pull the mass inward (radially toward the center). Since the string is the only horizontal force and the mass moves in a horizontal circle, the tension must point radially inward to provide the necessary centripetal acceleration. Choice A incorrectly suggests the tension points outward, which would cause the mass to spiral outward rather than maintain circular motion. The key principle is that the net force in circular motion must point toward the center to continuously redirect the velocity.
A 0.30 kg object moves at constant speed in a circle of radius 0.50 m on a horizontal surface. If the object's speed doubles, how does the required net force magnitude change?
Answer: It quadruples This question tests understanding of how centripetal force depends on speed. The centripetal force formula is F = mv²/r, showing that force is proportional to the square of speed. When speed doubles, the required centripetal force increases by a factor of 2² = 4, or quadruples. This quadratic relationship means small speed increases require much larger force increases. Choice B incorrectly assumes a linear relationship between force and speed. To solve problems about changing circular motion parameters, use the centripetal force formula to identify which variables change and how they affect the required force.
A 0.10 kg object moves at constant speed in a horizontal circle of radius 0.40 m on a string. The object's speed doubles while the radius stays the same. How does the required inward net force change?
Answer: It becomes four times as large This question tests understanding of how centripetal force depends on speed. The centripetal force formula is F = mv²/r, showing that force is proportional to the square of the speed. When speed doubles while mass and radius remain constant, the required inward force becomes four times as large (C). This quadratic relationship means that small increases in speed require much larger increases in centripetal force. The force doesn't just double (A) because of the v² term, and it certainly doesn't stay the same (B) or decrease (D). Remember that centripetal force increases with the square of speed - doubling speed quadruples the required force.
A 2.0 kg mass moves in a horizontal circle of radius 1.0 m at constant speed. Which change would increase the magnitude of the centripetal acceleration?
Answer: Increase the speed while keeping radius constant This question tests understanding of factors affecting centripetal acceleration. The centripetal acceleration formula is a = v²/r, showing acceleration increases with speed squared and decreases with radius. To increase acceleration magnitude, either increase speed (choice D) or decrease radius. Increasing radius (choice C) would decrease acceleration, while decreasing speed (choice B) would also decrease it. Mass doesn't appear in the acceleration formula, so changing mass (choice A) doesn't affect acceleration. When analyzing how to change centripetal acceleration, use a = v²/r to identify which changes increase or decrease the acceleration magnitude.
A student twirls a rubber stopper on a string in a horizontal circle at constant speed. The speed doubles while the radius stays the same. How does the required centripetal force change?
Answer: It increases by a factor of 4 This question tests understanding of the centripetal force formula in circular motion. The centripetal force required for circular motion is given by F = mv²/r, where m is mass, v is speed, and r is radius. When speed doubles (v → 2v) while mass and radius remain constant, the force becomes F = m(2v)²/r = 4mv²/r, which is four times the original force. This quadratic relationship with speed means doubling speed requires quadrupling the force. Choice A incorrectly suggests a linear relationship between speed and force. The key strategy is to use the centripetal force formula and recognize that force depends on the square of speed.

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