Osm Physics by Ashish

Motion Relative to Earth (Rotating Frame) Earth is a non-inertial (rotating) frame , so we add fictitious forces to apply Newton's laws. 1. Centrifugal Force (affects g ) Cause: Earth's rotation (every object, moving or not). Direction: Radially outward from the axis. Effect on g: g ′ = g − ω 2 R cos ⁡ 2 λ g ′ = g − ω 2 R cos 2 λ 2. Coriolis Force (affects moving objects) Cause: Motion relative to rotating Earth. Formula:   F ⃗ c o r = − 2 m ( ω ⃗ × v ⃗ ) F cor ​ = − 2 m ( ω × v ) Direction: Perpendicular to motion; does no work (changes direction only). Deflection: Right in N. Hemisphere, Left in S. Hemisphere. Examples: Cyclones, ocean currents, trade winds, Foucault pendulum, projectile drift.

Rotating Frame of Reference and Coriolis Force Let the coordinates of any point P are $(x,y,z)$ and unit vectors are $(\hat{i},\hat{j},\hat{k})$ along the axes of the stationary reference frame S. The position vector of point P is $$ \overrightarrow{OP}=\vec r =\hat{i}x+\hat{j}y+\hat{k}z \tag{1} $$ Fig. (1): Rotating reference frame R If another reference frame R which is initially at $t=0$ coincident with the frame S, is rotating with an angular velocity $\vec{\omega}$. After $t$ seconds all the axes of frame R will be inclined by an angle ($\theta=\omega t $) with the respective axes of frame S. In this state if the coordinates of the same point P are $(x',y',z')$ and unit vectors are $(\hat{i}',\hat{j}',\hat{k}')$ along the axes of the rotating reference frame R, then the position vector of point P is $$ \overrightarrow{OP}=\vec r' =\hat{i}'x'+\hat{j}'y'+\hat{k}'z' \tag{2} $$ Since the dir...