Calculator · Engineering Mechanics
Rigid-Body Impulse–Momentum Calculator
Impulse and momentum for ONE planar rigid body: the linear balance J = m(v_G2 − v_G1) and the angular balance about the centre of mass, K_G = I_G(ω₂ − ω₁) with K_G = ∫M_G dt.
Mode
Linear Impulse–Momentum
Results
| Relation used | J = m (v_G2 − v_G1) = Δp |
|---|---|
| Momentum before, p₁ = m·v_G1 | (2, 4) kg·m/s |
| Momentum after, p₂ = m·v_G2 | (8, -2) kg·m/s |
| Change Δp | (6, -6) kg·m/s |
| Required impulse J | (6, -6) N·s |
| Magnitude |J| | 8.4853 N·s |
Technical reference
J = m·(v_G2 − v_G1)
K_G = I_G·(ω₂ − ω₁) = ∫M_G dt
H_G = I_G·ω
- J
- linear impulse of the resultant force[N·s]
- K_G
- angular impulse of the resultant moment about G[N·m·s]
- H_G
- angular momentum about G[kg·m²/s]
- I_G
- mass moment of inertia about the axis through G[kg·m²]
The angular balance H_G = I_G·ω and its impulse form K_G = ΔH_G are what a rigid body adds over the particle Impulse–Momentum relation: a spinning body carries angular momentum even when v_G is unchanged, and a moment impulse changes ω independently of the linear balance.
Both balances are for one rigid body only; eccentric impact and two-body contact are out of scope, as the constant-load mode's Δt and resultant loads make explicit.
Assumptions
- · One planar rigid body. Momentum in kg·m/s and impulse in N·s are equal in value here but are reported as distinct quantities.
- · The angular balance is taken about the centre of mass G, counter-clockwise positive, with K_G = ∫M_G dt.
- · The constant-load mode assumes the resultant force and the resultant moment about G are both constant over the whole of Δt.
- · Eccentric impact, contact impulse, restitution at a contact point and two colliding bodies are deliberately not modelled: they need an impact model this tool does not have.
Continue
The two-state modes fix a change of momentum, not the loads that produced it, so there is no complete model to carry into a Lab. Use the constant-load mode for that.