Uncategorized: Practice Problem & Solution
A particle moves in x-y plane according to rule \(x = a sin omega ttext{ and }y = a cos omega ttext{. The particle follows: (2010 Mains)}\
Solution Explained:
To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:
Concept: Parametric equations of motion define the trajectory.
Formula: \(sin^2 theta + cos^2 theta = 1\).
Given \(x = a sin omega ttext{ and }y = a cos omega t\).
Square and add: \(x^2 + y^2 = (a sin omega t)^2 + (a cos omega t)^2 = a^2 (sin^2 omega t + cos^2 omega t) = a^2\).
This is the equation of a circle \(x^2 + y^2 = a^2\).
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