Further kinematics

Circular motion, Simple harmonic motion, thermal

Condition for applying the simple pendulum equation

The angle of maximum displacement is less than 10 ° because a small angle approximation is used

Specific heat capacity

The amount of energy to increase the temperature of 1kg of a substance by 1K

Specific latent heat

The amount of energy required to change the state of 1 kg of substance without changing its temperature 

Internal energy 

The sum of randomly distributed kinetic and potential energy of the particles in a given system 

Two conditions of simple harmonic motion

1. Acceleration is directly proportional to displacement 

2. Acceleration is in the opposite direction of displacement

   a=−ω^2x

Damping

Energy in an oscillation is lost to the environment, leading to reduced amplitude of oscillations 

Light damping

Amplitude of damping gradually decreases by a small amount each oscillation

Critical damping

The amplitude is reduced to zero in the shortest time possible without oscillating

Heavy damping

The amplitude reduces slower than critical damping but also without any oscillations

Free vibration

No external force is continuously acting on the system so it oscillates at its natural frequency

Forced vibration 

The system experiences an external driving force which cause it to oscillate 

Resonance

• The amplitude of oscillations of the system drastically increase due to gaining an increase amount of energy from the driving force

• Occurs when the driving frequency is equal to the natural frequency of the system

Application of resonance

• Instruments — flute has a long tube in which air resonates creating a stationary sound wave

• Radio — tuned so that its electric current resonates at the same frequency as the desired broadcast frequency 

• Swing — the pushing forces provides a driving frequency which causes resonance and allows it to swing higher

Assumptions in the kinetic theory model (ideal gas)

1. No intermolecular forces act on molecules

2. The motion of molecules are random and collisions are perfectly elastic

3. The duration of collisions are negligible

4. The molecules move in straight lines between collisions

5. Particles has no potential energy

Boyle’s law

Pressure is inversely proportional to volume at a constant temperature

Charles’ law

Volume is directly proportional to temperature at constant pressure

Pressure law

Pressure is directly proportional to temperature at constant volume