# Angular rotation velocity and acceleration

## Homework Statement

A small object with mass 3.55 kg moves counterclockwise with constant speed 1.55 rad/s in a circle of radius 2.70 m centered at the origin. It starts at the point with position vector 2.70 m. Then it undergoes an angular displacement of 8.50 rad.

v=ωr
a=rω^2

## The Attempt at a Solution

I've calculated the new position vector of -1.63i + 2.16j and know it's in the second quadrant at 127 degrees but can't get the correct answer of -3.34i + (-2.52)j m/s for it's velocity. The equation I'm using for i is 2.7*sin(127+90) and I'm using 2.7*cos(127+90) for j and neither of these end up and the correct answer. What am I doing wrong?

## Answers and Replies

Simon Bridge
Science Advisor
Homework Helper
You described the situation, but have not given the question.

Have you been asked to give the tangential velocity in cartesian co-ordinates?

1st draw the situation.

Do all your angles in radiens.
(Learn to think in radiens - definition: put a circle with a radius of one unit so it's center is on the point of an angle ... the size of the angle is the distance around the circumference that is inside the angle.)

It's gone 8.5radiens from the start so it's gone around more than once (how many radiens in a circle?)

The angle of the velocity is $\pi/2$ around from this - use the drawing to figure out which way. Draw it in. Choose the easy angles on the sketch to work out the components.