Calculator · Engineering Mechanics
Rigid-Body Work–Energy Calculator
Work–Energy for a planar rigid body. The kinetic energy is always shown as a translational part ½m|v_G|² and a rotational part ½I_Gω², never as one collapsed number, and T₂ − T₁ = W_net is used in whichever direction is known.
Mode
Body
About the axis through G, in kg·m² — not an area second moment.
Initial state
Final state
Results
| Relation used | T = ½m|v_G|² + ½I_Gω² and T₂ − T₁ = W_net |
|---|---|
| Translational KE, T₁ = ½m|v_G1|² | 9 J |
| Rotational KE, ½I_Gω₁² | 8 J |
| Total kinetic energy T₁ | 17 J |
| Translational KE, ½m|v_G2|² | 25 J |
| Rotational KE, ½I_Gω₂² | 18 J |
| Total kinetic energy T₂ | 43 J |
| Change ΔT = T₂ − T₁ | 26 J |
| Net work W_net | 26 J |
Work of the loads
Two constant-load work terms, as an aid. They are not added to W_net automatically: enter the value you want to use above.
| Work of the couple, W_M = M·Δθ | 15.708 J |
|---|---|
| Work of the force, W_F = F · Δr | 10 J |
| Sum of these two terms | 25.708 J |
M is a moment in N·m and Δθ is in radians; their product is an energy in J. The two units are kept distinct even though they share a dimension.
Technical reference
T = ½·m·|v_G|² + ½·I_G·ω²
T₂ − T₁ = W_net
- T
- total kinetic energy of the rigid body[J]
- v_G
- speed of the centre of mass[m/s]
- ω
- angular velocity about the axis through G[rad/s]
- I_G
- mass moment of inertia about that axis[kg·m²]
- W_net
- net work done by the applied loads over the interval[J]
The rotational term ½·I_G·ω² is what distinguishes this from the particle Work–Energy relation, T = ½·m·v²: a rigid body stores kinetic energy in its spin as well as its translation, and the two parts are always reported separately, never as one collapsed number.
Assumptions
- · Planar rigid-body motion; T = ½m|v_G|² + ½I_Gω² with ω about the axis through G.
- · |v_G| is a speed: work–energy is insensitive to the direction of v_G.
- · The energy equation fixes the magnitude of a solved rate only; the sense of rotation is stated, not discovered.
- · The work of a force uses the displacement of its own point of application. An eccentric force never silently uses the displacement of G.
- · A negative required squared speed is reported as no physical solution, never as a number.
Continue
Work–Energy fixes speeds, not directions or loads, so there is no complete state to carry into the Rigid-Body Dynamics Lab. Set up the load system there directly, or use the interval work–energy check inside its Energy & Momentum view.