Uniform circular motion and centripetal force

Equipment

• 3D model of a body circling on a tilted plane with v and a vectors
• Sliders for radius r and speed v
• Mass slider m in the force section
• Readout of centripetal acceleration and force

Procedure

1. Watch velocity and acceleration vectors

   Run the first section: the vector $v$ stays tangent to the orbit while $a$ always points to the center, perpendicular to $v$. Though speed is constant, the velocity direction changes continuously — that is why acceleration exists.

2. Check $a_c = v^2/r$

   Keep r fixed, raise v through two values and read $a_c$: doubling v quadruples $a_c$. Then hold v and raise r: $a_c$ drops inversely. Compare readings with $a_c = v^2/r$; at fixed angular speed $\omega$, $a_c = \omega^2 r$ grows with r.

3. Measure centripetal force versus mass

   In section two, hold v and r then raise m: the required centripetal force grows linearly per $F_c = mv^2/r$. Change v at fixed m and predict the new $F_c$ before reading it; note centripetal force is a real net force (tension, friction, gravity), not a new kind of force.

Simulation

Experiment history

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