6 Classic Mechanics Traps: Pendulum on a Swing, Lift Free-Fall, Earth Rotation & Feather-Coin Drop
How UPSC & State PSCs test $T = 2\pi\sqrt{l/g}$, apparent weight, and Earth’s angular velocity.
- 1. Girl Swinging on a Swing Stands Up: Her Centre of Gravity (CG) shifts upward ⇒ effective length (l) of the pendulum decreases ⇒ Time Period (T = 2\pi\sqrtl/g) decreases, so the swing oscillates FASTER!
- 2. Pendulum Clock in Summer vs Winter & In Orbit: In summer, thermal expansion lengthens the metal rod (l ↑ ⇒ T ↑), so the clock loses time (runs slow). Inside an artificial satellite or free-falling lift (geff = 0), T = ∞, so a pendulum clock stops working completely (astronauts must use spring-driven or quartz watches!).
- 3. What Happens if Earth Stops Rotating?: At the Equator, effective gravity is g' = g - \omega^2 R. If Earth stops rotating (\omega = 0), weight of objects at the Equator increases, whereas weight at the Poles remains completely unchanged!