Vedatom Physics Mechanics / Rotational Mechanics
◈ Simulations ▤ Full book
Reading a rotation right
Torque is a vector, τ = r × F. Only the component of the force perpendicular to r turns the body; the right-hand rule fixes the sign — counter-clockwise positive.
Moment of inertia lives with an axis. The same body has a different I about every axis, so always name the axis before quoting a number. I about the CM is the minimum for any parallel family.
Rolling links v and ω. Rolling without slipping means v = ωr, so the kinetic energy splits as ½mv²(1 + k) with k = I/mr². Contact-point friction does no work.
L is conserved when net torque is zero. Draw mass inward and ω rises to hold L = Iω fixed — but KE is not conserved; muscles pay for it.
watch the rolling race · §04
full primer ↗
Mechanics · all fourteen modules inked · all lit
§01

Torque — the turning of a force

A force turns a body only through its lever arm — the perpendicular distance from the axis to the line of action. Push straight along the rod and nothing turns; push square to it and you get the full τ = rF sin θ. Slide the grip point out, change the pull, or swing its angle and watch the lever arm — and the torque — respond.

Bench · a force on a wrench
r⊥ = {{ tq.rperp }} m F = {{ tqF }} N axis
lever length r{{ tqR }} m
force F{{ tqF }} N
angle θ (r to F){{ tqTheta }}°
torque τ = r · F · sin θ
{{ tqTau }} N·m
{{ tqNote }}