Centre of mass, centre of gravity and stability – plumb line and toppling
PhysicsForces & DynamicsAges 15–16
Loading…
Sign in to playThree screens: place point masses on a rod or a plane, choose which ones are inside the system boundary and watch the centre of mass x_cm = Σm·x/Σm move; a virtual practical that hangs a lamina from two or three holes and draws along a plumb line, so the centre of gravity is where the lines cross, with a results table and the error; and a block whose base width and centre-of-gravity height you can change, tilted until it topples when the line of action of its weight passes outside the base.
Lesson: Centre of mass of a system of particles, centre of gravity, finding the centre of gravity of a lamina with a plumb line, stability and toppling
What it shows
The centre of mass of a system is the mass-weighted average position of its parts: x_cm = Σm·x / Σm. Which objects count depends on where you draw the system boundary. In a uniform gravitational field the weight acts at this point, the centre of gravity. A lamina hung from a pin settles with its centre of gravity directly below the pin, so plumb lines drawn from two holes cross at the centre of gravity. An object on a flat surface topples when the line of action of its weight passes outside its base: a wide base and a low centre of gravity make it more stable.
How to use
Centre of mass: drag the masses, change Mass of the selected one and tick In the system in the table. Plumb line: choose a Lamina, hang it from hole A, B or C, wait until it is still and press Mark plumb line; repeat for another hole. Stability: set Base width b, Height H and Height of centre of gravity h, then tilt the block and press Let go, or press Find toppling angle.
Parameters you can change
- Screen Centre of mass of point masses, Centre of gravity with a plumb line (practical), Stability and toppling angle
- Place the masses on A rod (one dimension), A plane (two dimensions)
- Number of point masses 2–5
- Shape of the lamina Irregular shape, L shape, Triangle
- Base width b 10–100 cm
- Height of the block H 20–150 cm
- Height of the centre of gravity h 5–145 cm
- Starting tilt angle θ 0–80 °
- Mass of the block m 1–50 kg
Questions to explore
- Which way does the centre of mass move when you take one mass out of the system, and why?
- Why do plumb lines drawn from two different holes cross at the centre of gravity of the lamina?
- To make a tall cupboard harder to tip over, should heavy things go on the top shelf or the bottom shelf?
