# Circular motion

1. Sep 17, 2005

Hi I really need help for this problem:

A mass is tethered to a post and moves in a circular path of radius r=.35m
on an air table -friction free- at a constant speed v=18m/s.
We employ the coordinate system ( classic 2 dimension space).
If at t=0s the mass is at θ=0o,
a-what is the coordinates(x,y) of the mass at t=0.1s?
b-what is thye acceleration vector at t=0s?
c-what is the acceleration vector of the mass when θ=90o?

Can someone help meI have noo idea!

a-(0.15m,-0.32m)
b-(-9.3*102m/s2)i
c-(-9.3*102m/s2)j

But first, i need to understand what is going on in the problem.

2. Sep 17, 2005

### joelperr

Circular motion problem

the first thing that you want to do for a problem of this type is to establish a proper coordinate system based on the problem and the contraints established. In your case, the problem is one of circular motion, and you are restricted to using Cartesian coordinates (incidentally, using polar coordinates is much more useful for problems involving any kind of circular path).

So, you should set up your Cartesian system, then show the path that the object traces out. Here, you should begin to see something.

Next, take all the information that is given to you in the problem, and try to make sense of it all. For example, the problem indicates what the radius of the circle is (which is useful, say, to find the circumference of the circle). Next, you are given the velocity of the mass (which is useful, say, to figure out how long it takes to go around the circumference of the circle). Moreover, you will also be able to find the angular velocity of the mass. Using this basic information and a little trigonometry, you should be able to solve the problem without a hitch; if not, post what you have done and we'll see where you got stuck.

--
joelperr

3. Sep 17, 2005

### HallsofIvy

Staff Emeritus
A circle of radius 0.35 m has circumference $0.7\pi$ m. At 18 m/s, the puck will complete a full circle ($2\pi$radians) in $\frac{0.7\pi}{18}$ seconds and so has an angular velocity of $\frac{2\pi}{\frac{0.7\pi}{18}}= \frac{36}{0.7}$ radians per second. That's about 51.43 radians per second.

What I would do (since this is in the college homework forum) is write the position vector as 0.35 cos(51.43t)i+ 0.35 sin(51.43t)j. The derivative of that is the velocity vector and the second derivative is the acceleration vector.