Question

A particle moves in x-y plane according to rule x = a sin ωt and y = a cosωt. What kind of path does the particle follow ?

(1) An elliptical path
(2) A circular path
(3) A parabolic path
(4) A straight line path inclined equally to x and y axes.

Answer 1

(2) A circular path.

Explanation:

As `x=asinomegat` and `y=acosomegat`

`sinomegat=x/a` and `cosomegat=y/a`

Hence squaring and adding

`sin^2omegat+cos^2omegat=x^2/a^2+y^2/a^2`

or `x^2/a^2+y^2/a^2=1`

or `x^2+y^2=a^2`

Hence, it is (2) A circular path.