Physics notes

Waves & SHM

Hooke’s law:

• The force exerted is proportional to the amount stretched from equilibrium

Equilibrium position:

• Location at the end of a spring when it is sitting at its natural length

Period of mass on spring:

• Amplitude does not matter. Stretching further increases speed which means period stays the same

Period of pendulum:

• Doesn’t depend on amplitude with SMALL angles. With large angles, sin x != x

Waves:

• A disturbance in a medium that transfers energy and momentum over significant distances

Transverse waves:

• Oscillation of the medium (direction of particles) is perpendicular to wave velocity (direction of wave)

Longitudinal:

• Oscillation is parallel to wave velocity

Y v.s X graph:

• Peak to peak is the wavelength

Y v.s T graph:

• Peak to peak is the period

Changing frequency:

• Does not affect the speed. Affects the wavelength

Changing speed:

• Need to change the properties of the medium. Amplitude does not affect

Doppler effect:

• Perceived frequency is different from the frequency from the speaker when they move

Source and observer moving closer:

• Wavelength decreases. Frequency increases.

Source and observer moving farther:

• Wavelength increases. Frequency decreases

Wave interference:

• When two waves overlap. Form a wave shape that’s the sum of both waves. D

Waves cancel:

• Destructive interference

Waves combine:

• Constructive interference

Combined value at point

• y = y1 + y2

After interference:

• Do not bounce. Keep going original path

Standing waves:

• Waves need to overlap and go different directions only if length and bounds of medium allow the wavelengths

Ends of strings:

• Fixed or loose

Fixed ends:

• Displacement nodes (no displacement)

Loose ends:

• Displacement antinodes (max displacement)

Beat frequencies:

• Waves with different frequencies overlap. Interference switches between constructive and destructive

Beat frequencies sound:

• Sounds like a wobble in the loudness

Torque and Angular Momentum

Rotational kinematics

• Need constant angular acceleration

Tangential acceleration

• Controls speeding up and slowing down. Will only have tangential & angular acceleration if this occurs

Centripetal acceleration

• Controls change in direction. Objects in a circle must have this

Torque:

• Causes angular acceleration. Need force to have torque

Forces:

• Exerted further from the axis of rotation increases torque. Vice versa. Perpendicular is the greatest. Angle between r & f

Equilibrium:

• Net torque and net force = 0

Rotational inertia:

• How much an object resists angular acceleration

Changing rotational inertia:

• Further mass distribution increases inertia and vice versa

Different objects:

• Varying moments of inertia. Inertia of hoop = inertia of mass on string

Rotational kinetic energy:

• Object rotating

When do objects have both kinetic energies:

• Object moving and rotating

Angular momentum:

• Conserved if not external torque. Even masses moving in a straight line can have angular momentum

Gravitational kinetic energy:

• Will always be negative, but can still be converted to kinetic energy

Rotational motion

Centripetal acceleration:

• Always points towards center of the circle

Centripetal forces

• Moving in a circular direction

Sum of centripetal forces:

• All forces pointing in and out of a circle. Tangential forces not included

Universal force of gravity:

• All masses pull and attract every other mass

Magnitude of forces:

• Always equal

Gravitational field:

• Vectors pointing in at a mass