Physics · University
Rotational dynamics and rolling constraints · revision notes
Angular velocity is the time derivative of angular displacement. For a fixed axis and constant moment of inertia, net torque equals I times angular acceleration.
Key ideas and conditions
Rotation
Angular velocity is the time derivative of angular displacement. For a fixed axis and constant moment of inertia, net torque equals I times angular acceleration.
Energy
Rigid-body rotation about a fixed axis has kinetic energy Iω²/2. A rolling body generally has both translational and rotational kinetic energy.
Constraints
For rolling without slipping, the centre speed equals Rω. That kinematic condition does not imply friction always dissipates energy.
Model limits
The moment of inertia depends on mass distribution and the chosen axis. A point-mass formula cannot replace the inertia of an extended object without justification.
Explain without looking
- For a fixed axis, what sets the sign of angular acceleration when I is positive?
- State two assumptions behind the equation τnet=Iα in its simple scalar form.
Further reading and review references
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