Mechanics

Angular Displacement (θ) The angle swept out by a radius vector as an object moves along a circular path. Measured in radians (rad), where one complete revolution equals 2π rad. Unlike linear displacement, angular displacement is a vector quantity (direction given by right-hand rule). For example, a point on a spinning fan blade moves through an angular displacement of 2π rad each full rotation. Angular Velocity (ω) The rate of change of angular displacement with respect to time. ω = Δθ/Δt for uniform motion. It is a vector pointing along the axis of rotation. In SI units, it is rad s⁻¹. A car's wheel rotating at 10 rad s⁻¹ means each point on the rim sweeps 10 radians per second. Centripetal Acceleration (ac) The acceleration directed toward the centre of the circular path, causing the change in direction of velocity. Even if speed is constant, the velocity vector changes direction, so acceleration exists. Its magnitude is ac = v²/r = ω²r. For a satellite in low Earth orbit, this acceleration is about 9.8 m s⁻² (equal to g), keeping it in circular motion.