UPCAT P6 - ROT. MOT. & WAVES

Angular velocity formula

ω = v/r (radians per second)

Angular velocity meaning

Rate of rotation; same ω for all points on a rigid spinning object, regardless of distance from center

Tangential velocity on a rigid disk

v = ωr; points farther from center move faster (linearly), same ω throughout

Centripetal acceleration formula

a_c = v²/r

Centripetal acceleration meaning

Acceleration directed toward the center; needed to constantly change direction in circular motion, even at constant speed

Why circular motion accelerates at constant speed

Velocity is a vector; direction keeps changing even if speed doesn't, so there is still acceleration

Torque formula

τ = F × r (r = distance from fulcrum)

Torque meaning

Rotational equivalent of force; same force farther from fulcrum = more torque

Balancing torques formula

M1a = M2b (clockwise torque = counter-clockwise torque, net torque = zero, no rotation)

Wave definition

Disturbance traveling through a medium, transferring energy (not mass)

Mechanical wave

Requires a medium to travel; e.g. sound wave, seismic wave

Electromagnetic wave

Does not require a medium; e.g. light, UV radiation

Crest

Maximum point above rest position

Trough

Maximum point below rest position

Amplitude

Maximum displacement from rest position; measures wave strength/intensity

Wavelength (λ)

Length of one complete wave cycle; measured crest-to-crest or trough-to-trough

One wave cycle

Crest → rest → trough → rest (back to starting position and direction)

Frequency (f)

Number of complete wave cycles passing a fixed point per second; unit = Hertz (Hz)

Wavelength vs frequency relationship

At constant wave speed: longer wavelength = lower frequency, shorter wavelength = higher frequency