hr-studioPhysics · 02
A computational design primer · Rigid Bodies

Now the shapes have size, and they spin.

A particle was a point. A rigid body has extent and orientation, so it carries an angle and a spin alongside its position — and a force applied off-centre both pushes it and turns it. That single idea, a lever arm, runs through mechanisms, toppling, and every simulation of solid things knocking into one another. Grab and fling anything.

Scroll to begin
i.

Push through the centre, or off it

A body spins around its centre of mass. Flick it straight through that centre and it only slides. Flick it off to one side and the same push becomes a torque — it slides and rotates. The turning effect is the force vector crossed with its offset from the centre: τ = r × F.

Drag from any point on the block and release to flick it.

Grab near the edge to make it spin
ii.

Why some things are hard to spin

Mass resists a push; moment of inertia resists a spin — and it depends on how the mass is spread out. The same twist gives a compact block a quick spin and a long bar a lazy one, because inertia grows with the square of the distance from the centre. Linear momentum is p = mv; its rotational twin is L = Iω.

Morph the shape, then hit Spin — same twist, very different result.

Compact spins fast · long spins slow
iii.

Bouncing changes the spin

When a body hits the floor, the reaction acts at the contact point, not the centre — so it delivers both a bounce and a twist. A block landing on one corner kicks its spin sideways; the bounce keeps a fraction of the incoming speed set by the restitution, never more. The dot marks the contact, the arrow the impulse.

Set how bouncy the floor is and watch it tumble.

Contact point · impulse arrow
iv.

Friction, gripping, and tipping over

At a contact, friction resists sliding up to a limit set by how hard the surfaces press together. Shove a block low with little friction and it skates; shove it high with plenty and it grips at the base and topples — because your push wins the tug-of-war of torques about the bottom corner. Then everything settles to rest.

Set the friction, then drag across the block to shove it.

Shove low to slide · high to tip
v.

The bin

Toss bodies into a bin and let them work it out. Under gravity they fall, collide, transfer momentum, and pack down into a settled heap — the painted spoke on each disc shows it spinning as friction bites. Tune how bouncy and how grippy the world is, tap to drop, drag to fling. This is packing, granular settling, and any pile of solid things, from one simple rule applied over and over.

Tap to drop · drag to fling
Give a shape a centre, an angle, and a spin, resolve every contact as an impulse with a lever arm, and solids tumble and stack exactly as they should. The lever arm is the whole difference between a point and a body.