Dynamics

Force: An agency that moves or tends to move, stops or tends to stop the motion of a body. It can also change the direction of motion.
Unit: Newton ($N$). It is a vector quantity.

Inertia: The property of a body due to which it resists any change in its state of rest or motion.
Dependence: Inertia depends on Mass. Greater mass means greater inertia.

Momentum ($P$): The quantity of motion possessed by a body due to its mass and velocity.
Formula: $P = mv$
Unit: $kg ms^{-1}$ or $Ns$ (Newton-second). Vector quantity.

A body continues its state of rest or of uniform motion in a straight line unless an external net force acts upon it.

When a net force acts on a body, it produces acceleration in the body in the direction of the net force.
Formula: $F = ma$
Unit of Force: One Newton (1N) is the force that produces an acceleration of $1 ms^{-2}$ in a body of mass $1 kg$.

To every action, there is always an equal and opposite reaction.
Action and Reaction forces act on different bodies.

Two bodies of masses $m_1$ and $m_2$ ($m_1 > m_2$) attached to a string passing over a frictionless pulley.

• Acceleration ($a$): $a = \frac{m_1 - m_2}{m_1 + m_2}g$
• Tension ($T$): $T = \frac{2m_1m_2}{m_1 + m_2}g$

Body $m_1$ moves vertically downward, body $m_2$ moves horizontally on a smooth surface.

• Acceleration ($a$): $a = \frac{m_1}{m_1 + m_2}g$
• Tension ($T$): $T = \frac{m_1m_2}{m_1 + m_2}g$

Friction: The force that opposes the motion of moving objects.
Limiting Friction ($F_s$): The maximum value of static friction.
Formula: $F_s = \mu R$ (where $\mu$ is coefficient of friction, $R$ is normal reaction).

Rolling Friction: The resistance encountered when a body rolls over a surface.
It is much less than sliding friction because the point of contact is negligible and no rupture of cold welds occurs.

• Advantages: Walking, writing, braking depend on friction.
• Disadvantages: Wear and tear of machines, energy loss as heat.
• Reducing Friction: Lubrication, using ball bearings, streamlining shapes.

Centripetal Force ($F_c$): The force that keeps a body moving in a circle. It always acts towards the center of the circle.
Formula: $F_c = \frac{mv^2}{r}$

Centrifugal Force: The reaction to the centripetal force. It acts outwards, away from the center. (Pseudo force in non-inertial frames).

• Banking of Roads: Outer edge raised to provide necessary centripetal force.
• Washing Machine Dryer: Spins fast; water droplets forced outward due to lack of centripetal force.
• Cream Separator: High speed rotation separates heavy milk from lighter cream.