Centripetal force – uniform circular motion on a string
PhysicsForces & DynamicsAges 15–16Virtual lab
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Forces & Dynamics
A mass m tied to a string of length R moves in uniform circular motion with angular speed ω (viewed from above). The velocity vector is always tangential, while the acceleration and string tension point toward the center with F = mω²R = mv²/R; the F(ω) graph is a parabola. Drag the mass to change the radius, slide the ω bar, or press Cut string to watch the mass fly off along the tangent. The Rotating disc screen adds a constant angular acceleration: set ω₀ and α, watch the θ(t), ω(t) and α(t) graphs, and compare v = rω, a_t = rα and a_c = ω²r for two markers at different radii.
Lesson: Uniform circular motion, centripetal acceleration, centripetal force
What it shows
An object moving in a circle at constant speed is still accelerating, because the direction of its velocity keeps changing: the acceleration a = ω²R = v²/R points to the centre, and here the string tension supplies the force F = mω²R. Doubling ω makes the tension four times larger, and cutting the string sends the mass along the tangent. The Rotating disc screen adds a constant angular acceleration α, so ω = ω₀ + αt and θ = ω₀t + ½αt². Every point of the disc shares θ, ω and α, but its speed v = rω, tangential acceleration a_t = rα and centripetal acceleration a_c = ω²r grow with its radius r.
How to use
On Mass on a string, change Angular speed ω in steps and note the tension to build a table of F against ω; drag the mass to change the radius and press Cut string to test a prediction. On Rotating disc, set Initial angular speed ω₀ and Angular acceleration α, press Run and watch the θ, ω and α graphs. Drag markers A and B, or use Radius of marker A and Radius of marker B, to compare v, a_t and a_c in the table.
Parameters you can change
- Mass 0.1–2 kg
- Orbit radius 0.2–2 m
- Angular speed ω 0.5–10 rad/s
- Show v, a, F vectors
- Screen Mass on a string, Rotating disc
- Initial angular speed ω₀ 0–10 rad/s
- Angular acceleration α -2–2 rad/s²
Questions to explore
- After the string is cut, why does the mass move along the tangent rather than straight outwards?
- Keeping ω fixed, how does the centripetal force change when the radius is doubled?
- If the angular speed is doubled, by what factor does the string tension increase?
