Calculator · Engineering Mechanics
Rotational Dynamics Calculator
ΣM_G = I_G·α for planar rigid-body rotation. I_G is a mass moment of inertia in kg·m² about the axis through the centre of mass — not an area second moment in m⁴.
Known values
Positive counter-clockwise, taken about the centre of mass.
Results
| Relation used | α = ΣM_G / I_G |
|---|---|
| Resultant moment ΣM_G | 20 N·m |
| Mass moment of inertia I_G | 5 kg·m² |
| Angular acceleration α | 4 rad/s² |
| Sense of α | Counter-clockwise |
Technical reference
ΣM_G = I_G·α
- ΣM_G
- resultant moment (torque) about the centre of mass G, CCW positive[N·m]
- I_G
- mass moment of inertia about the out-of-plane axis through G[kg·m²]
- α
- angular acceleration, CCW positive[rad/s²]
This is the rotational half of the planar equations of motion; the engine also implements ΣF = m·a_G for translation of G, but this calculator solves only the moment-inertia-α relation, one term at a time.
I_G must come from the Mass Moment of Inertia about the same axis through G, in kg·m² — an area second moment (m⁴) is a different quantity and is rejected. See the Mass Moment of Inertia calculator.
Assumptions
- · Planar motion, with moments taken about the centre of mass G.
- · I_G is strictly positive and is a mass moment of inertia in kg·m².
- · The moment is the resultant of every applied load; individual eccentric forces are reduced in the Rigid-Body Dynamics Lab.
- · A moment that varies with orientation is outside this relation, which holds at one instant.
Continue
The same I_G with the moment carried as a free couple, so α stays constant and the rotation is exact. The mass and any eccentric loads are yours to add.