kg$\cdot$m/s

Momentum is a vector quantity; its direction is the same as velocity.

Greater mass or velocity means greater momentum.

Newton's Second Law: Force is the rate of change of momentum.
Formula: $F = \Delta p / \Delta t = (mv_f - mv_i) / t$
$\Delta p$ = change in momentum, $t$ = time over which force acts.
A larger force changes momentum faster.
A longer time period reduces the force needed (safety features like airbags, seatbelts).

Definition: Change in momentum of an object when a force is applied over time.
Formula: Impulse ($J$) $= F \times t = \Delta p$
Units: Newton-seconds (N$\cdot$s) or kg$\cdot$m/s.
A shorter impact time leads to greater force.
A longer impact time reduces force, making collisions safer (e.g., airbags, cushioned helmets).

The total momentum of a system remains constant if no external force acts on it.
Total momentum before collision = total momentum after collision.
Applies to collisions and explosions.
Momentum is conserved in both elastic and inelastic collisions.
Formula: $m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$
$m_1, m_2$: masses of objects
$u_1, u_2$: initial velocities
$v_1, v_2$: final velocities

Increase Collision Time ($\Delta t$): Use materials that deform or compress (e.g., foam, airbags) to spread out the impact over a longer time.
Reduce Impact Force ($F$): Spread the force over a larger area (e.g., helmets with padding).
Examples:
- Helmets: Cushioned interiors increase impact time, reducing force on skull.
- Airbags: Inflate to cushion impact, increasing time of impact.
- Parachutes: Increase air resistance, slowing descent and reducing impact force.
- Crumple Zones in Cars: Designed to absorb energy by controlled deformation.

Definition: A force that opposes the motion of an object when it comes into contact with a surface.
Acts parallel to the contact surface and opposite to the direction of motion.
Caused by surface roughness and intermolecular forces.
Two types: Rolling friction and sliding friction.

Aspect	Rolling Friction	Sliding Friction
Definition	Friction when an object rolls over a surface	Friction when an object slides over a surface
Cause	Caused by deformation of surfaces at contact points	Caused by interlocking of rough surfaces
Magnitude	Smaller compared to sliding friction	Larger because more surface contact creates resistance
Practical Use	Wheels, ball bearings reduce friction	Brakes in vehicles create sliding friction to stop

Rolling friction is weaker than sliding friction, which is why wheels and ball bearings are used to reduce friction.