Homework Help: Path Coordinates and constant circular acceleration.

1. Sep 25, 2008

Buckshot23

1. The problem statement, all variables and given/known data

A top is made to spin by unwinding the string wrapped around it. The string has a length of 0.64m and is wound at a radius of 0.02m (neglect string thickness). The string is pulled such that top spins with a constant angular acceleration of 12 rad/s^2. Determine the velocity and acceleration vectors in path coordinates when the string has completely unwound. Assume that the top starts from rest.

2. Relevant equations

a=(tangential acceleration)*$$\hat{t}$$+(normal acceleration)*$$\hat{n}$$

v=(magnitude of velocity vector)*$$\hat{t}$$
3. The attempt at a solution

The string pulls so that 16$$\pi$$ revolutions occur which is approximately 315.8 radians.

Tangential acceleration = r*$$\alpha$$ or (.02m)(12 rad/s^2) (or is this only for constant circular speed situations?)

I am pretty well lost on this one. Where do I begin?

2. Sep 25, 2008

LowlyPion

First are you sure that it's 16*π is the number of revolutions?

As to figuring the velocity maybe you can use the usual kinematic equations?

Vf2 = Vo2 + 2*a*x