Physics

Momentum

Momentum is a measure of an object's inertia in motion. It is defined as the product of an object's mass and its velocity.

The equation for momentum is:p=mvp=mv

Impulse

a measure of the "effort" put into changing an object's momentum. It is defined as the product of the net force acting on an object and the time interval over which that force acts.

The equation for impulse (JJ) is:J=FtJ=Ft

Impulse-Momentum Theorem

The impulse-momentum theorem states that the net impulse applied to an object is equal to the change in its momentum. This is a direct consequence of Newton's second law.

ΣFt=mΔvΣFt=mΔvΣFt=ΔpΣFt=Δp

Conservation of Momentum

The law of conservation of momentum states that in a closed system (where no external forces act), the total momentum remains constant. This means that the total momentum before a collision or interaction is equal to the total momentum after the collision or interaction.

Conservation in Two Directions

Momentum is conserved in all directions independently. For a collision in two dimensions, we consider the conservation of momentum in the x-direction and the y-direction separately.

Torque

Torque is the rotational equivalent of force. It is a measure of how effectively a force can cause an object to rotate about an axis. Torque depends on the magnitude of the force, the distance from the pivot point to the point where the force is applied (lever arm), and the angle between the force vector and the lever arm.

Equilibrium

when the net force and the net torque acting on it are both zero.

Conditions:

1. Net Force is Zero: ΣF=0ΣF=0 (for both x and y directions)

2. Net Torque is Zero: Στ=0Στ=0

Angular velocity (ω)

the rate of change of angular displacement (ΔθΔθ).ω=Δθtω=tΔθ​

Angular acceleration (α)

the rate of change of angular velocity.α=Δωtα=tΔω​

Moment of inertia (I)

the rotational equivalent of mass. It measures an object's resistance to changes in its rotational motion. It depends not only on the object's mass but also on how that mass is distributed relative to the axis of rotation. Mass further from the axis of rotation contributes more

Simple Harmonic Motion (SHM)

is a type of periodic motion where the restoring force is proportional to the displacement from equilibrium and acts in the opposite direction.

Waves

Waves transfer energy through a medium or space.

Transverse Waves:

The disturbance is perpendicular to the direction of wave propagation (e.g., light waves, waves on a string).

Longitudinal Waves:

The disturbance is parallel to the direction of wave propagation (e.g., sound waves)

Frequency (f):

number of waves that pass a point per second (units: Hz).

Period (T)

• The time it takes for one full wave to pass a point (units: s).

Wave Speed (v):

The speed at which the wave propagates

Wave Superposition:

When two or more waves meet, their amplitudes add together at each point.

Constructive Interference:

Amplitudes add to create a larger amplitude.

Destructive Interference:

Amplitudes of opposite signs add to create a smaller amplitude.

Standing Waves:

Formed by the superposition of two waves traveling in opposite directions, resulting in points of no displacement (nodes) and maximum displacement (antinodes).

Intensity:

The rate at which energy is delivered per unit area.

Sound Waves:

Longitudinal waves that travel through a medium.

Pitch:

related to frequency (high frequency = high pitch).

Loudness

Related to amplitude/intensity (large amplitude = loud sound).

Timbre:

The unique quality of a sound, determined by the combination of fundamental and harmonic frequencies.

Doppler Effect

The apparent change in frequency of a wave due to relative motion between the source and observer.

Pascal's Principle:

Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. This is the basis of hydraulic systems:

Buoyant Force and Archimedes' Principle:

An upward buoyant force (Fb​) is exerted by a fluid on an immersed object. This force is equal to the weight of the fluid displaced by the object.

Poiseuille's Law:

Describes laminar flow through a pipe.