Rotational inertia and τ = Iα – turntable lab, angular momentum and rolling
PhysicsForces & DynamicsAges 15–16
Loading…
Sign in to playA virtual lab on rotational dynamics. A falling mass on a string wound round a drum turns a rod with two movable masses, a solid disc or a ring; a light gate times the fall so you can find the angular acceleration α, the torque τ and the moment of inertia I = τ/α, with a results table, an α–τ graph and energy bars. The Angular momentum screen lets you pull masses in on a spinning turntable or drop a ring onto it; the Rolling screen races a hoop, a hollow sphere, a solid cylinder and a solid sphere down an incline.
Lesson: Rotational dynamics: torque, moment of inertia, angular acceleration, rotational kinetic energy and angular momentum
What it shows
A torque makes an object spin faster in the same way a force makes it speed up: τ = Iα. The moment of inertia I depends on how the mass is spread about the axis, I = Σmr², so moving masses outwards or using a ring instead of a disc makes the same torque produce less angular acceleration. A falling mass loses gravitational potential energy, which becomes its own kinetic energy plus rotational kinetic energy ½Iω² and work against friction. With no external torque, angular momentum L = Iω is conserved.
How to use
On the τ = Iα lab tab, choose a Rotor, set the Hanging mass m, Drum radius r and Drop height h, and press Release; each run adds a row to the table. Repeat with different m and read I from the α against τ graph. On the Angular momentum tab, press Spin, then drag a mass or use Distance R, or press Drop ring. On the Rolling tab, set the Incline angle and press Release.
Parameters you can change
- Screen τ = Iα lab, Conservation of angular momentum, Rolling down an incline
- Rotor Rod with 2 masses, Solid disc, Ring
- Hanging mass m 20–500 g
- Drum radius r 1–4 cm
- Mass of each sliding mass 50–400 g
- Distance of the masses from the axis R 4–24 cm
- Mass of disc or ring M 0.2–2 kg
- Radius of disc or ring R 5–20 cm
- Drop height h 0.3–1 m
- Friction in the bearing
- Incline angle θ 5–40 °
Questions to explore
- Why is the torque from the string m(g − a)r rather than mgr, and when are the two nearly equal?
- How do the moment of inertia and the angular acceleration change when the masses move from 20 cm to 10 cm?
- Why does a solid sphere roll down the slope faster than a hoop of the same mass and radius?
