System of Particles and Rotational Motion
Class 11 · Physics
4 ideas in Class 11 Physics, explained in plain words, with games and quizzes to practise.
Centre of Mass
Part of: Mass Centres and Turning Forces
The centre of mass is the balance point where all mass can be imagined to sit. Symmetry puts it at the geometric centre of uniform bodies; otherwise it is the mass-weighted average of positions. Outside pushes move it as if all mass sat there, while inside pulls cancel.
Why it matters. Whole-body motion, from bursts to balances, follows this one point. It separates what the outside world changes from what it cannot.
Formulas
- X = (m1 x1 + m2 x2) / (m1 + m2)
- Motion of the balance point follows F = M a
Key words
- Centre of mass
- : The balance point where all mass can be imagined to sit.
- Mass-weighted average
- : Positions averaged with masses as weights.
- Total momentum
- : Mass of the system times centre-of-mass speed.
- Internal forces
- : Pushes between parts that cancel and cannot shift the balance point.
Try it in two minutes
- Balance a ruler on a finger to find its middle.
- Weigh two ends of a loaded stick and guess the shift.
- Push a toy and watch its middle travel straight.
Try at home. Balance a spoon with a lump of dough at spots along it.
Torque, Angular Momentum and the Vector Product
Part of: Mass Centres and Turning Forces
A twist needs force times lever length, which is torque. Spin is captured by angular momentum, and torque is its rate of change. Both come from the cross product of two arrows, whose size carries the sine of the angle between them.
Why it matters. Doors, spanners and tops all obey twist rules. The cross product is the language of anything that turns.
Formulas
- Torque = r F sin(angle)
- L = r p = m v r for a circling mass
- Torque = rate of change of angular momentum
Key words
- Torque
- : Force times lever length, the twist on a body.
- Lever arm
- : The distance from the pivot to the force line.
- Angular momentum
- : Spin content, distance times linear momentum.
- Cross product
- : The product of two arrows whose size carries the sine of their angle.
Try it in two minutes
- Open a door at the handle, then near the hinge.
- Twist a lid with short and long grips.
- Spin a tied ball and feel the steady pull.
Try at home. Loosen a nut with fingers, then with a spanner, and compare.
Equilibrium and Moment of Inertia
Part of: Balance, Spin Energy and Rolling
A body rests when both total force and total twist vanish. Spinning resistance is moment of inertia, the sum of each bit of mass times its squared distance from the axis. Rings beat discs of the same size because their mass sits farther out.
Why it matters. Still bridges, steady ladders and quick wheels all depend on these two ideas. Shape matters as much as mass.
Formulas
- I = sum of m r^2 over the body
- Hoop about centre: I = M R^2
- Disc about centre: I = (1/2) M R^2
Key words
- Translational equilibrium
- : Zero net force, so the centre stays put or glides steadily.
- Rotational equilibrium
- : Zero net torque, so the spin stays unchanged.
- Moment of inertia
- : Mass times squared distance from the axis, summed over the body.
- Axis of rotation
- : The fixed line a body spins about.
Try it in two minutes
- Balance a scale with unequal coins at unequal arms.
- Spin a coin and a bangle to compare effort.
- Lean a ruler on a wall and feel the foot push.
Try at home. Balance two different masses on a ruler pivot.
Rolling Motion and Rotational Energy
Part of: Balance, Spin Energy and Rolling
Rolling is centre travel plus spin about the centre, with rim speed matching travel speed. Its energy splits into moving and spinning parts. Spin energy is half moment of inertia times spin rate squared, and spin momentum stays fixed without outside twists.
Why it matters. Wheels, balls and races down ramps all split energy this way. It explains why shape decides the winner.
Formulas
- Rolling condition: v = r w
- Rotational energy = (1/2) I w^2
- Total rolling energy = (1/2) M v^2 + (1/2) I w^2
Key words
- Rolling without slipping
- : Travel where rim speed matches centre speed.
- Rotational kinetic energy
- : Spin energy, half moment of inertia times spin rate squared.
- Contact point
- : The rim spot touching the ground, instantly at rest.
- Conservation of angular momentum
- : Spin momentum stays fixed without outside twists.
Try it in two minutes
- Roll a coin and watch its centre glide while it turns.
- Race a ring against a disc down a slope.
- Mark one rim point and trace its looping path.
Try at home. Race cans full and empty down a safe slope and compare.
What your child will practise
- Centre of Mass: Ocean Quick Fire (Quick Fire)
- Equilibrium and Moment of Inertia: Jungle Puzzle (Clue Puzzle)
- Equilibrium and Moment of Inertia: Jungle Quick Fire (Quick Fire)
- Rolling Motion and Rotational Energy: Candy Quick Fire (Quick Fire)
- Torque, Angular Momentum and the Vector Product: Desert Puzzle (Clue Puzzle)
- Quiz: Centre of Mass (8 questions)
- Quiz: Equilibrium and Moment of Inertia (8 questions)
- Quiz: Rolling Motion and Rotational Energy (8 questions)
- Quiz: Torque, Angular Momentum and the Vector Product (8 questions)