Physics Regents Notes

1. Mechanics

Kinematics (Motion in One Dimension)

• Distance vs. Displacement:

  • Distance: A scalar quantity representing the total path length traveled, without regard to direction.

  • Displacement: A vector quantity, representing the straight-line distance from the initial position to the final position, along with the direction.

  • Example: If you walk 3 meters east and then 4 meters west, the total distance is 7 meters, but the displacement is 1 meter west.

• Speed vs. Velocity:

  • Speed: Scalar quantity, rate at which an object moves. Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}.

  • Velocity: Vector quantity, rate of displacement. Velocity=DisplacementTime\text{Velocity} = \frac{\text{Displacement}}{\text{Time}}.

• Acceleration:

  • Change in velocity over time.

  • Formula: a=ΔvΔta = \frac{\Delta v}{\Delta t}, where Δv\Delta v is the change in velocity, and Δt\Delta t is the time interval.

  • Units: m/s2\text{m/s}^2

  • Can be positive (speeding up) or negative (slowing down).

• Equations of Motion (For Uniformly Accelerated Motion):

  • v=v0+atv = v_0 + at — Final velocity is the initial velocity plus acceleration times time.

  • d=v0t+12at2d = v_0 t + \frac{1}{2} a t^2 — Distance traveled is the initial velocity times time plus half of acceleration times time squared.

  • v2=v02+2adv^2 = v_0^2 + 2ad — Final velocity squared is the initial velocity squared plus two times acceleration and distance traveled.

• Free Fall:

  • Acceleration due to Gravity: All objects in free fall near Earth’s surface experience the same acceleration due to gravity, g=9.8 m/s2g = 9.8 \, \text{m/s}^2 (ignoring air resistance).

  • Objects in free fall have downward acceleration and speed up as they fall.

2. Newton's Laws of Motion

• First Law (Law of Inertia):

  • An object at rest stays at rest, and an object in motion stays in motion with constant velocity unless acted upon by an unbalanced force.

  • Inertia: The tendency of an object to resist changes in motion. The more massive an object, the greater its inertia.

• Second Law (Force and Acceleration):

  • Formula: F=maF = ma, where:

    • FF is the net force (in newtons, N),

    • mm is the mass (in kilograms, kg),

    • aa is acceleration (in m/s²).

  • This law explains that the force applied to an object is directly proportional to the acceleration produced and inversely proportional to the object's mass.

• Third Law (Action and Reaction):

  • For every action, there is an equal and opposite reaction.

  • Example: When you push on a wall, the wall pushes back with the same force in the opposite direction.

• Friction:

  • Static Friction: The force that resists the initiation of sliding motion between two surfaces. It is greater than kinetic friction.

  • Kinetic Friction: The force that resists the movement of two objects sliding past one another.

  • Frictional Force Equation: Ff=μFnF_f = \mu F_n, where:

    • FfF_f is the frictional force,

    • μ\mu is the coefficient of friction (depends on the materials in contact),

    • FnF_n is the normal force (the force perpendicular to the surface).

3. Work, Energy, and Power

• Work:

  • Formula: W=Fdcos⁡(θ)W = Fd \cos(\theta), where:

    • WW is work (in joules, J),

    • FF is the force applied (in newtons, N),

    • dd is the displacement (in meters, m),

    • θ\theta is the angle between the force and the direction of displacement.

  • Work is done when a force moves an object in the direction of the force.

• Kinetic Energy (KE):

  • Formula: KE=12mv2KE = \frac{1}{2} mv^2, where:

    • mm is the mass (in kilograms, kg),

    • vv is the velocity (in meters per second, m/s).

  • The energy an object possesses due to its motion.

• Potential Energy (PE):

  • Gravitational Potential Energy: Energy stored due to an object's position in a gravitational field.

  • Formula: PE=mghPE = mgh, where:

    • mm is the mass (kg),

    • gg is acceleration due to gravity (9.8 m/s²),

    • hh is the height (in meters, m).

• Conservation of Energy:

  • Energy cannot be created or destroyed, only transformed from one form to another.

  • Total mechanical energy (E=KE+PEE = KE + PE) remains constant in an isolated system unless external forces (like friction) do work on the system.

• Power:

  • Formula: P=WtP = \frac{W}{t}, where:

    • PP is power (in watts, W),

    • WW is work (in joules, J),

    • tt is time (in seconds, s).

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

4. Momentum

• Momentum (p):

  • Formula: p=mvp = mv, where:

    • mm is the mass of the object (in kg),

    • vv is the velocity of the object (in m/s).

  • Momentum is a vector quantity, and it represents the "motion" of an object.

• Impulse:

  • Formula: J=FΔtJ = F \Delta t, where:

    • JJ is impulse (in newton-seconds, N·s),

    • FF is the force applied (N),

    • Δt\Delta t is the time interval during which the force acts (in seconds).

  • Impulse is the change in momentum, which occurs when a force acts over a period of time.

• Conservation of Momentum:

  • In an isolated system (no external forces), the total momentum remains constant.

  • pinitial=pfinalp_{\text{initial}} = p_{\text{final}}

5. Circular Motion

• Centripetal Force:

  • Formula: Fc=mv2rF_c = \frac{mv^2}{r}, where:

    • FcF_c is the centripetal force (N),

    • mm is the mass (kg),

    • vv is the velocity (m/s),

    • rr is the radius of the circular path (m).

  • The force directed towards the center of a circular path, keeping the object in motion.

• Centripetal Acceleration:

  • Formula: ac=v2ra_c = \frac{v^2}{r}

  • The acceleration of an object moving in a circular path, directed toward the center of the circle.

6. Gravitation

• Newton’s Law of Universal Gravitation:

  • Formula: F=Gm1m2r2F = G \frac{m_1 m_2}{r^2}, where:

    • FF is the gravitational force between two masses (N),

    • GG is the gravitational constant (6.67×10−11 Nm2/kg26.67 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2),

    • m1m_1 and m2m_2 are the masses of the objects (kg),

    • rr is the distance between the centers of the two masses (m).

• Gravitational Potential Energy:

  • Formula: PE=−Gm1m2rPE = - \frac{G m_1 m_2}{r}

  • Negative sign indicates that the gravitational potential energy decreases as the two masses move closer together.

7. Waves and Optics

• Wave Properties:

  • Wavelength (λ\lambda): The distance between two consecutive peaks or troughs in a wave (in meters, m).

  • Frequency (ff): The number of waves passing a point per second (in hertz, Hz).

  • Amplitude: The maximum displacement from the equilibrium position. Larger amplitude means more energy.

  • Wave Speed: v=fλv = f \lambda, where:

    • vv is the wave speed (m/s),

    • ff is the frequency (Hz),

    • λ\lambda is the wavelength (m).

• Sound Waves:

  • Sound is a longitudinal wave, meaning that the particles of the medium vibrate parallel to the direction of wave propagation.

  • The speed of sound depends on the medium; it travels faster in solids than liquids and faster in liquids than gases.

• Light Waves:

  • Reflection