Rotational Equilibrium and Rotational Dynamics

[ataglance05]

Homework Statement

Question Details:
A 10 kg engine is rotating at the rate of 20 rad/sec about a point on a wire 3 meters in length with a working tensile strength of 1.8*106 N. The engine is fired and produces an acceleration of 1 rad/sec2. What's the maximum possible ω (angular velocity) (in other words: 1) whats's the fastest ω which doesn't break the wire?) 2)How long should the engine be fired to reach the maximum possible ω? 3)How far will the engine travel in meters while it's accelerating to the maximum possible ω?

Homework Equations

The Attempt at a Solution

I believe it's right, however this is only #1. Need help on #2 and #3.

Thanks!

 

[andrevdh]

2 can be solved with the equation

$$w_f = w_i + \alpha t$$

since the angular acceleration is sustained as long as the engine is firing. The intial angular speed is 20 and the final is 245 rad/s. Once you solved for the time use it in the other equation that will give the angle in radians that it turned through during the burn. Using the radius you can then calculate the total distance covered during this time.