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Chapter 3 · 3.7 Circular motion (extension)
Circular Motion Lab: Horizontal, Vertical & Conical
A 3D lab you can walk around: whirl a mass in a horizontal circle, swing it round a vertical circle, or send it round as a conical pendulum. Tension, weight, velocity and the resultant centripetal force are drawn to scale and update live; resolve the tension into T cos θ and T sin θ, drop below √(gr) to watch the string go slack at the top, or cut the string and see the mass leave along the tangent. Every practice-question setup is one click away.
3D ApparatusTension now:
Loading the 3D apparatus…
Drag to rotate · scroll or pinch to zoom · grid squares are 25 cm
Velocity vTension TWeight mgNormal force NResultant (centripetal) force
Force arrows are drawn to the same scale as each other.
1.00 m
1.50 s
0.50 kg
Speed
From the practice questions
Readouts
Speed v = 2πr / t
4.19 m/s
Turns per minute
40.0
Centripetal acceleration v²/r
17.5 m/s²
Tension T = mv²/r
8.77 N
Angular speed ω
4.19 rad/s
Weight mg (balanced by N)
4.90 N
F = mv² / r
with v = 2πr / t, where t is the time for one turn
Try This
- →Cut the string. Does the ball fly outwards, or carry on along the tangent?
- →Halve the time per turn: the speed doubles and the tension goes up four times.
- →Double the mass: the motion looks the same, but the string must pull twice as hard.
What Each Variable Means
r
Radius
Distance from the centre of the circle to the mass, in metres (m).
v
Speed
Distance round the circle each second (m/s). The direction keeps changing, so the velocity does too.
t
Time for one turn
The period of the motion, in seconds (s). One turn covers the circumference, 2πr.
T
Tension
The pull of the string, in newtons (N). Here it is the only horizontal force, so it is the centripetal force.
F
Centripetal force
The resultant force towards the centre that keeps the mass on the circle: F = mv²/r.