Rotation and Angular Momentum: Solving for thrust of a rocket

engineer08

1. A solid bar of length L = 0.5m and with W = 0.1m weighs 2kg. It also has two constant-thrust rockets attached on either end. Each rocket is small enough to be considered a point mass of 0.25kg. If the bar is initially at rest and in two seconds after the rockets are fired it achieves a rotation rate of 1000rpm, determine the thrust of each rocket.



2. Relevant equations
torque = I * angular acceleration
I = (1/12)*(L^2+W^2)*M



3. I found I, angular momentum, to be 0.0542. I am not sure what to do from there.

diazona

I is moment of inertia, not angular momentum.

What equation do you know that relates torque and angular momentum (which is usually written L)?

engineer08

Correct my apology, I is moment of inertia. An equation I know that relates torque with angular momentum 'L' is:

torque = dL/dt = d(Iw)/dt

The acceleration changed from 0 to 1000rpm in 2 seconds. and L=Iw, which is the angular velocity times the moment of inertia. I'm confused as to what to do

diazona

It's not acceleration that changed from 0 to 1000rpm in 2 seconds

Think about this: what else can you calculate from that 1000rpm figure?

engineer08

So, angular velocity changes from 0 to 1000rpm in 2 seconds, and we know I. I can therefore solve for angular momentum, right? Couldn't you also integrate the sum of the moments exerted by each rocket from time t to 0? I still am not sure how to translate all of this to the thrust of each rocket.

diazona

Right, try that.

By the way, you do know what kind of physical quantity thrust is, right?

engineer08

thrust must be in Newtowns (N), presumably? I was pretty certain of that.

diazona

Yep, just checking.