How to Use the Circular Motion Simulator
 

Scenario

• Horizontal Circle: a mass on a string swings in a flat circle.

• Vertical Circle: a mass on a string swings in a vertical loop, so its speed and tension change around the circle.

• Banked Turn: a car rounds a banked curve, with or without friction.

• Conical Pendulum: a mass hangs from a string and sweeps out a cone.

• Satellite Orbit: a satellite circles a planet, held in orbit by gravity.
  Note for teachers: The key question in every scenario is the same: what is actually providing the centripetal force? Ask students to name it for each one before they look at the force vectors.
   

Mode

• Explore lets you change the variables freely. Lab lets you collect and graph data. Challenge tests your calculations.
   

Parameters

• The parameters change with each scenario:

  • Horizontal Circle: mass, radius, speed, and gravity.

  • Vertical Circle: mass, radius, launch speed at the bottom (v_b), and gravity.

  • Banked Turn: car mass, curve radius, bank angle (θ), coefficient of friction (μ), car speed, and gravity.

  • Conical Pendulum: mass, string length (L), half-angle (θ), and gravity.

  • Satellite Orbit: a planet preset (Earth, Venus, Moon, Mars, Jupiter, or Saturn), altitude (h), planet mass and radius, and satellite mass.
     

Display & Readout

• Force vectors draws the forces acting on the object, and Labels adds their names and values.

• The Readout panel also changes with each scenario. For example, Horizontal Circle shows the centripetal force, angular speed (ω), and period (T). Vertical Circle shows the tension at the bottom and top of the loop and the minimum launch speed needed to complete the loop. Banked Turn shows the ideal speed along with the maximum and minimum speeds friction allows.

• Use Theme to switch between Dark and Light mode.
  Mastery tip: In the Vertical Circle, slowly lower the launch speed toward the minimum loop speed and watch the tension at the top. At the minimum speed, gravity alone provides the centripetal force at the top and the tension drops to zero.
   

Lab Mode

• Each scenario has its own lab. Two variables are held constant and you vary one independent variable:

  • Horizontal Circle: vary the radius with mass and speed fixed. Plot Fc vs 1/r. The slope is mv².

  • Vertical Circle: vary the launch speed with mass and radius fixed. Plot tension at the bottom vs v_b². The slope is m/r.

  • Banked Turn: vary the bank angle with the radius fixed. Plot v_ideal² vs tan θ. The slope is gr.

  • Conical Pendulum: vary the half-angle with the string length fixed. Plot T² vs cos θ. The slope is 4π²L/g.

  • Satellite Orbit: vary the altitude with the planet fixed. Plot v² vs 1/r. The slope is GM.

• Set your independent variable with its slider and click Record data point. Repeat across a wide range of values.

• Once you have enough data points, the simulator fits your data and reports the slope, intercept, and R². Compare that slope to the one you derived from the equation.
  Mastery tip: Before you collect data, derive why that particular graph should be linear. Each lab is set up so that the slope equals a combination of the constant variables.
  Note for teachers: The Satellite Orbit lab confirms that the slope of v² vs 1/r is GM. That ties circular motion directly to universal gravitation.
   

Challenge Mode

• Each challenge lists the given values for the current scenario and asks you to find one unknown, such as the speed, the tension at the bottom of a loop, the ideal banking speed, the period of a conical pendulum, or a satellite's orbital speed.

• Enter your answer in the units shown and click Check answer. Use New Challenge for another problem.

• Switch scenarios to practice each type of problem.
  Mastery tip: Start every problem with a free body diagram, then set the net inward force equal to mv²/r.