Physics · Simulator 006
Spin a ball on a string around a circle. Change the radius, speed and mass to see the centripetal acceleration and the tension the string must supply, then cut the string to see which way the ball flies.
An object moving at constant speed v on a circle of radius r is still accelerating, because its direction keeps changing. The acceleration points to the centre:
a_c = v² / r = ω² r, ω = v / r, T = 2πr / v
Some real force must supply F_c = m v² / r. Here it is the string tension, because the motion is drawn in a horizontal plane with gravity ignored. There is no outward “centrifugal” force acting on the ball in this frame. If the string is cut, nothing pulls inward, so the ball moves in a straight line along the tangent (Newton's first law).
Turn on speed changes to add a tangential acceleration. The total acceleration then has a tangential part as well as the centripetal one.
Assumes a light, inextensible string, a horizontal circle, no gravity sag and no air resistance.
A 0.2 kg ball on a 0.8 m string can take at most 20 N of tension. What is the fastest speed it can be whirled at?
v_max = √(F·r/m) = √(20 × 0.8 / 0.2) = √80 ≈ 8.94 m/s. Set m = 0.2 kg and r = 0.8 m, then raise v until the tension reads 20 N.