ΣM=Iα is the rotational analogue of F=ma.
ΣM_G=I_Gα for rotation about the centre of mass, together with ΣF=ma_G. For fixed-axis rotation ΣM_O=I_Oα. Rotational kinetic energy is ½Iω².
A 2 kg·m² flywheel under 10 N·m accelerates at 5 rad/s².
Rotational dynamics is the rotational form of Newton's second law, so it is needed for motors, flywheels, turbines and any spinning part.
ΣM=Iα is the rotational analogue of F=ma.
Rotational dynamics is the rotational form of Newton's second law, so it is needed for motors, flywheels, turbines and any spinning part.
Moment of inertia, which measures how mass is distributed relative to the rotation axis.
There is no angular acceleration, so a spinning body keeps rotating at a constant rate, unless friction or other torques act.
Typical applications include finding the angular acceleration of a motor shaft under a given torque, designing the inertia of a flywheel for speed smoothing and predicting the spin-up time of a centrifuge.
Study "Instantaneous centre of rotation" first (topic 35 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Torque causes angular acceleration. Larger I gives slower response. Used for wheels, pulleys and shafts.
A 2 kg·m² flywheel under 10 N·m accelerates at 5 rad/s².
The next topic is "Mass moment of inertia", which builds directly on this one.
It is classed as Beginner in Engineering Mechanics (topic 36 of 106). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
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