Path Coordinates and constant circular acceleration.

[Buckshot23]

Homework Statement

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.

Homework Equations

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

v=(magnitude of velocity vector)*$$\hat{t}$$

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?

 

[LowlyPion]

Homework Statement

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.

Homework Equations

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

v=(magnitude of velocity vector)*$$\hat{t}$$

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?

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

Only V is in radians/s and x is in radians?