Time to rotate system 20 degrees

[D.B0004]

Homework Statement

In the system of Problem 2-6, we need move the load by 20 degrees and bring the system to rest. Assuming a triangular speed profile of the load with equal acceleration and deceleration rates (starting and ending at zero speed). Assume a coupling efficiency of 100%. The magnitude of the electromagnetic torque (positive or negative) available from the motor is 500 Nm.

nL/nM= 3
JL = 8.3 kg*m2
JM = 1.4 kg*m2

What is the time (in seconds) needed to rotate the load by an angle of 20o? Give the correct answer to 3 or more decimal places.

Homework Equations

T(em) = [Jm + (Wl/Wm)^2 * Jl]*dw/dt

The Attempt at a Solution

I see a dt in there so I think this is my hint. I know I can set T(em) to 500. Jm is given, and I believe W (omega) of load is 3 times smaller than the motor, w/w would be (1/3)^2. But dw/dt is constant due to the triangle torque constraint isn't it? Cant integrate that right? Could someone explain how I am thinking of this wrong with a push in the right direction? Thanks.

 

[Simon Bridge]

In the system of Problem 2-6,...

Where is problem 2.6 and what is the system it proposes?

 

[D.B0004]

Where is problem 2.6 and what is the system it proposes?

Im sorry. I completely forgot to add those! See file attached.

 

[D.B0004]

Im sorry. I completely forgot to add those! See file attached.

Wow and now I posted the WRONG PICTURE. Thought I only had one screen shot.

 

[D.B0004]

This problem probably shouldn't be in the introductory section...but hey maybe someone will get it.

 

[D.B0004]

Here are equations listed below the figure.

 

[haruspex]

I believe W (omega) of load is 3 times smaller than the motor

In the time the motor rotates once, how often does the load rotate?

dw/dt is constant

It's constant during each of the two phases, acceleration and deceleration.

Cant integrate that right?

Constants are the easiest of all to integrate.