Question

Determine an expression for the position vector of a particle that starts on the positive y axis at t=0 (i.e., at t=0, (x0,y0)=(0,R)) and subsequently moves with constant ω. Express your answer in terms of R, ω, t, and unit vectors i^ and j^.

Answer 1

Answer:

$\vec r = R(-cos\omega t \hat i + sin\omega t\hat j)$

Explanation:

Let say the particle starts in counterclockwise direction with constant angular speed

so the angle turned by the particle after some time is given as

$\theta = \omega t$

now the x and y components of the position of the particle is given as

$x = R sin\omega t$

$y = R cos\omega t$

now we know that it starts in counter clockwise direction so we will have position vector given as

$\vec r = x\hat i + y\hat j$

$\vec r = R(-cos\omega t \hat i + sin\omega t\hat j)$