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Relative Velocity
V CP= V CE- V PE
Kinematics
Velocity
Acceleration
Displacement
S=S0+V0t+at2/2
SUVAT- Equations of motion (1 dimension)
Projectile’s Laws of Motion
• The horizontal component of the velocity is constant
Vx = Vo cosӨ
• The vertical component is given by
Vy = Vo sinӨ - gt
• The displacement along the x - axis is
X = Vo cosӨ * t
• The displacement in the y - direction is
Y = Vo sinӨ t – gt2/2
Dynamics
Force. F = ma
Work Done
For constant force:
For variable force:
Instantaneous Power:
Average Power:
Kinetic Energy (K E):
Total mechanical energy
E = KE + PE
Momentum:
=m
Impulse
Conservation of momentum
Work Done by Conservative Force
Potential Energy
Conservative force vs Potential Energy
Torque
Conditions of equilibrium
Σ F = 0
Σ t = 0
Position of the Center of Mass
Friction
|Ff|= μ|N|
μk < μs.
Work Done by Friction
W = Ff d cosθ
Angular acceleration
ω(t) = dθ/dt
Radial vector
=cos θ
Tangential vector
= - sinθ
Radius vector
= r =
Tangential Velocity
=
Tangential Acceleration
=
Centripetal Force
Rotational Kinetic Energy
Angular acceleration
L = Iω
Torque
Work done by torque
W = τθ
Power by torque
Work – Kinetic Energy by torque
Linear and Angular Equations comparison table
Simple harmonic motion.
Force
Acceleration for spring and pendulum
Angular frequency
Equation of SHM
Equation for period for spring and pendulum
Frequency
Maximum speed and acceleration in SHM
vmax = Aω amax = Aω2
Energy in SHM
Total energy in SHM
Maximum KE and PE
Damping oscillations
Periodic Driving Force
Waves
The equation of a moving sine wave
Velocity of the wave
Travelling wave function
Propagation speed in string
Intensity of the sound wave
Intensity level (Loudness)
Standing waves function
Frequencies of the string
Path difference for constructive interference
δ = ml
Path difference for destructive interference
δ = (m + ½) l
Young’s double slit experiment and Diffraction grating
For bright fringe
For dark fringe
Single slit diffraction
Reflection
Refraction
Snell’s Law of Refraction
Wave moving from medium 1 to medium 2:
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