2. Kinematics, dynamics and energy of material points

Kinematics

the study of motion without considering the forces causing it

Dynamics

The study of motion and the forces that cause it

initial velocity

"u" stand for

displacement

"s" stand for`

vavg= ∆x/∆t

formula for average velocity (vavg)

v=u+at

equations for motion (for constant acceleration):

formula for velocity (v)

ut+1/2​at²

equations for motion (for constant acceleration): What is the formula for displacement

u²+2as

equations for motion (for constant acceleration): What is the formula for veloity² (v²)

(u+v)/2 t

equations for motion (without constant acceleration): What is the formula for displacement (s)

Newtons 2nd Law

The acceleration of a moving object depends upon its mass and the force acting on it

Fnet=ma

formula for Newtons second law

Newtons 3rd Law

for every action there is an equal and opposite reaction

W=mg (where g=Acceleration due to gravity)

formula for Weight

Ff=μN, where μ is the coefficient of friction and N is the normal force

formula for Friction Force

Fc=mv²/r, where r is the radius of the circle in the question

formula for centripetal force

FΔt=Δp=mv−mu

formula for the impulse-momentum theory

W=Fdcosθ

formula for Work Done by a Constant Force

KE=1/2mv2

formula for Kinetic Energy

GPE=mgh, where m= mass, g= gravitational acceleration h=height of the an object

formula for Gravitational Potential Energy

Wnet=ΔKE

formula for Work-Energy Theorem

P=W/t or P=Fv

formula for Power

Rest

No change in position.

Uniform Linear Motion (Constant Velocity)

Constant speed in a straight line. Zero acceleration.

Non-Uniform Linear Motion

Velocity changes (either speed or direction). Nonzero acceleration.

Uniformly Accelerated Motion

Constant acceleration in a straight line.

Uniform Circular Motion

Constant speed in a circular path, but changing velocity due to continuous change in at is direction.

Displacement (Δx or s)

Change in position (vector quantity).

Distance

Total path length covered (scalar quantity: magnitude only w no direction).

Velocity (v)

Rate of change of displacement (vector).

Speed

Magnitude of velocity (scalar).

Acceleration (a)

Rate of change of velocity (vector).

Mechanical Work

The transfer of energy resulting from a force acting over a distance. It's the trajectory effect of the force acting on the body.

Kinetic Energy (KE)

Energy due to motion.

Potential Energy (PE)

Stored energy due to position or configuration.

Gravitational Potential Energy (GPE)

Energy stored due to an object's height in a gravitational field. It depends on mass, gravitational acceleration, and height. It specifically depends on the gravitational acceleration.

Power

The rate at which work is done or energy is transferred.

Inertial Frame

A non-accelerating reference frame (whose point of view are we measuring this movement) where Newton's First Law holds true. A free material point(not subject to any external forces or constraints.) remains at rest or in uniform linear motion.

Non-Inertial Frame

An accelerating reference frame where Newton's First Law does not hold. A free material point would appear to be in uniformly accelerated motion without an external force.

Gravitational Force (Weight)

The force of attraction between any two objects with mass. On Earth, it's mg.

Normal Force

The force exerted by a surface perpendicular to it, preventing an object from passing through.

normal force is the push a surface gives back to an object that's resting on it, acting straight out from the surface, to stop the object from falling through.

Friction Force

A force that opposes motion between surfaces in contact.

Centripetal Force

A net force that acts towards the centre of a circular path, causing an object to move in a circle. It is perpendicular to the instantaneous velocity and in the same direction as the instantaneous acceleration (centripetal acceleration).

Combining Forces

Multiple forces acting on a material point:(hypothetical object with mass but no size or internal structure) can be replaced by a single force (resultant force) using the vector sum of forces.

Dynamics of a Material Point

Investigates the cause of its movement.

Force Definition

A force is determined by its magnitude and direction