The position vector of a particle moving in the x - y plane at time t is r → = a 1 – cos ⁡ ω t i ^ + a sin ⁡ ω t j ^ . The path of the particle is :

Question

TestHub · Accepted Answer

Particle is moving in a circle of radius $a$ and centre $(a, 0)$ with constant angular velocity $ω$ . At time $t = 0$ particle is at origin and it starts rotating clockwise. At time t it has rotated an angle $θ$ given by

$θ = ω t$

$y = a \sin θ = a \sin ω t$

and $x = a - a \cos θ = a (1 - \cos ω t)$

$∴ \vec{r} = a (1 - \cos ω t) \hat{i} + a \sin ω t \hat{j}$

Physics - Circular Motion Question with Solution | TestHub

Options:

Doubts & Discussion