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Topic 2.9: Practice Sheet — Circular Motion

Name: _______________________________ Date: _______________ Period: ______

Directions: For every problem, identify which real force (or combination of forces) is providing the centripetal force before writing any equation, and solve symbolically before substituting numbers.

  1. A ball moves in a circle of radius $2.5\text{ m}$ at a constant speed of $6.0\text{ m/s}$. Find its centripetal acceleration.
  2. A $0.20\text{ kg}$ ball on a string moves in a horizontal circle of radius $0.80\text{ m}$ at $4.0\text{ m/s}$. Find the tension in the string. (Assume the string is horizontal — ignore gravity's effect for this problem.)

Vertical Loop

  1. A roller coaster car of mass $250\text{ kg}$ goes around the top of a vertical loop of radius $6.0\text{ m}$. Find the minimum speed at the top so the car maintains contact with the track.

Banked Curve

  1. A frictionless banked curve has radius $80\text{ m}$ and is banked at $25°$. Find the speed at which a car can round it with no reliance on friction.

Conceptual (Practice-Sheet Depth)

  1. A ball on a string swings in a horizontal circle while the string traces out a cone shape, attached to a fixed point above (a "conical pendulum"). Sketch a free-body diagram of the ball, showing tension and gravity. Explain which direction the NET force must point, and why.

Kepler's Third Law Reasoning

  1. Planet X orbits its star at 4 times the orbital radius of Planet Y. Using $T^2 \propto r^3$, find the ratio of Planet X's orbital period to Planet Y's orbital period (i.e., $T_X / T_Y$).

Justify a Claim

  1. A classmate claims: "A car going around a circular curve at constant speed has zero net force acting on it, since its speed isn't changing." Explain why this claim is incorrect, using the definitions of velocity and acceleration.

AP Classroom-Style Questions

(Modeled directly on the real Topic 2.9 AP Classroom quiz question styles — graph reasoning, ranking, and orbital-motion applications.)

  1. Bottom of a Vertical Loop. A sled slides along a vertical circular track of radius $r$ with negligible friction. At the bottommost point of the track, the sled has speed $v_b$. Write a symbolic expression for the normal force the track exerts on the sled at the bottommost point, in terms of $m$, $v_b$, $r$, and $g$. Then describe the shape of a graph of that normal force plotted against $v_b$ (is it linear? does it pass through the origin?).
  2. Tangential vs. Centripetal. A cart moves along a horizontal circular track. At a certain instant, the cart is speeding up. A classmate claims the net force on the cart at that instant must point exactly toward the center of the track. Explain why this claim is incorrect, and describe the actual direction of the net force.
  3. Orbital Speed vs. Radius. A satellite orbits Earth in a circle of radius $R$ with orbital speed $v$. The satellite is moved into a new circular orbit of radius $3R$. Using $v=\sqrt{GM/r}$, find the new required orbital speed in terms of $v$.
  4. Linked Wheels. Two wheels connected by a drive belt (like a bicycle's gears) turn together without slipping, so any point on the belt — and therefore the outer edge of each wheel — moves at the same tangential speed $v$. Wheel A has radius $2r$ and Wheel B has radius $r$. Find the ratio of their periods, $T_A/T_B$, and explain your reasoning in terms of $T=2\pi r/v$.

Keep this sheet — it's part of your semester study materials, same as your Concept Sheets.