System of Particles and Rotational Motion
Centre of mass, torque, angular momentum and moment of inertia.
What is System of Particles and Rotational Motion?
Mass-weighted average position that moves as if all mass were concentrated there and all external forces acted at that point
Key formula / rule: Rotational dynamics
Key points
- Relate torque, moment of inertia and angular momentum, and locate the centre of mass of a system
Common exam trap
Using a moment of inertia for the wrong axis without the parallel axis theorem
Definitions
- Name
Centre of mass
- Definition
Mass-weighted average position that moves as if all mass were concentrated there and all external forces acted at that point
- Name
Torque and inertia
- Definition
Torque τ = r x F in N m is the rotational analogue of force; moment of inertia I = sum m r2 in kg m2 depends on the axis
- Name
Exam insight
- Definition
With no external torque, I ω is conserved — why a spinning skater speeds up on pulling the arms in
- Name
Worked example
- Definition
Disc of 2 kg, R = 0.5 m: I = (1/2)MR2 = 0.25 kg m2, so τ = 0.5 N m gives α = 2 rad/s2
Learning objectives
Relate torque, moment of inertia and angular momentum, and locate the centre of mass of a system
Formulae
- Name
Rotational dynamics
- Expression
τ = r F sin(θ) = I α; L = I ω
- Name
Centre of mass
- Expression
Rcm = (sum mi ri)/(sum mi)
Common mistakes
Using a moment of inertia for the wrong axis without the parallel axis theorem
Omitting rotational kinetic energy for a rolling body
Keywords
system of particles
centre of mass
torque
moment of inertia
angular momentum
rotational motion