Find coordinate on circumference

Question

Consider a body starts moving in a circular motion with linear velocity 0.02 m/s and angular velocity 0.3 rads/s. If it's initial coordinates on Cartesian plane are x=5 and y=5, where would the body be after 5 seconds in terms of coordinates?

Answer 1

With the additional information from the comments the problem can be solved in the following way:

1. Calculate the radius $r$ of the circular motion by using $\omega\cdot r = v$. Here, $\omega$ is the angular velocity and $v$ is the velocity.

2. Calculate the center point of the circular motion.

3. Calculate the total angle covered in 5 seconds: $\varphi=\omega\cdot5$.

4. Use trigonometric functions or vector algebra to deduce the endpoint of the motion after 5 seconds.

Hope that helps! :-)

Answer 2

Assuming the motion in clockwise direction, we have

• $x-x_0=R\cos (\omega \cdot t)$
• $y-y_0=-R\sin (\omega \cdot t)$

with

• $\omega=0.3$ rad/s
• $v=\omega\cdot R=0.02$ m/s $\implies R=\frac {2}{30}$m

where $(x_0,y_0)$ are the coordinates of the center of motion lying on the line $y=x$ such that the distance form $(5,5)$ is equal to $R$.

Note that assuming the motion couterclock wise we can fine another valid solution.