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# Average torque watch

1. If some one could help me understand this I would be very grateful..

An early form of four-stroke gas engine stores kinetic energy in a large flywheel driven by the
crankshaft. The engine is started from rest with its load disconnected and produces a torque which
accelerates the flywheel to its off-load running speed of 110 rev min–1.

(a) The flywheel has a moment of inertia of 150 kgm2 and takes 15 s to accelerate from rest to an
angular speed of 110 rev min–1.
(i) Show that the rotational kinetic energy stored in the flywheel at this speed is
approximately 10 kJ. (done)

(ii) Calculate the average useful power output of the engine during the acceleration.
.........
This is where I am having trouble when they say average Id thought you need to divide by 2 the ms doesnt do that ................................ ................................ ................................ ................................ .......
................................ ................................ ................................ ................................ ..............
(iii) Use your answer to part (ii) to calculate the average net torque acting on the flywheel
during the acceleration.

then they continue to this part and then divide the angler velocity (w) by 2 this time and to find the torque

When the engine is running at 110 rev min–1 off-load, the gas supply to the engine is suddenly
cut off and the flywheel continues to rotate for a further 35 complete turns before coming to rest.
Calculate the average retarding torque acting on the flywheel.

and yet this time they dont divide by 2 anywhere..

Im utterly confused what they mean by average (i know the accelartion is not constant so you find the average ) but when to divide by 2 and when not to I have no clue..
If someone can help I will be grateful thanks
2. Average is used because it isn't a constant power.
It's a bit like average speed equals total distance divided by total time.
Average power would be total energy gained by flywheel divided by time taken to do it. (P=E/t)
As the angular velocity goes from zero to w, the average is w/2
(The power didn't go from zero to some known value)
3. (Original post by Stonebridge)
Average is used because it isn't a constant power.
It's a bit like average speed equals total distance divided by total time.
Average power would be total energy gained by flywheel divided by time taken to do it. (P=E/t)
As the angular velocity goes from zero to w, the average is w/2
(The power didn't go from zero to some known value)
hmm ..ok but what about the last question it goes from 110 revs^-1 to 0 ( for the average retarding torque), cant why cant we use w/2 there?
4. You haven't said how they did the last bit, but the way I would do it would be to say that the average torque times the number of revs (expressed in radians) equals the work done in bringing the wheel to rest. IE. Loss in rotational KE.
The best way of understanding this is to think of the linear velocity equivalents of this.
In that last part, the equivalent for linear would be force times distance is work done (loss in KE). [Compare with torque time angle turned through is work done; loss in rotational KE]

If I asked you what force managed to stop a car with KE 1000J in a distance of 10 meters, you would use Force times 10m = 1000J
The force calculated would actually be an average because we don't know if it is always constant. It's like calculating what the force would be if it was constant. That's what average means here. It's exactly the same for rotation.

average power = total work done divided by total time taken.
average speed = total distance travelled divided by total time taken

In both cases you are saying that the "average" is the force/speed that it would have been if it was a constant value. That's what average means here.
(In reality the value probably varies up and down a bit around the average, but it doesn't matter; it's a definition)

On the other hand, if you know something goes from zero to say 100 uniformly, you know the average value was 50.
In the cases where they divide by 2, that's the assumption. The angular velocity in this case was assumed to go uniformly from nothing to w.
5. (Original post by Stonebridge)
You haven't said how they did the last bit, but the way I would do it would be to say that the average torque times the number of revs (expressed in radians) equals the work done in bringing the wheel to rest. IE. Loss in rotational KE.
.. I used
which (v^2=u^2+2as)

thanks very much for the help so far

Edit : actually reading through it again , I get it ..thanks
6. (Original post by rbnphlp)
.. I used
which (v^2=u^2+2as)

thanks very much for the help so far

Edit : actually reading through it again , I get it ..thanks

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