Why Does Angular Speed Not Increase Indefinitely in Rotating Systems?

[fog37]

Hello Forum,

If a net nonzero torque is applied to an object that is able to rotate, the object will spin at an increasing angular speed. The torque causes angular acceleration.

In the case of a car engine, the engine eventually spins at a max constant rotational speed omega. Why does the angular speed not continue to increase due to the applied torque? Is it simply because as the speed increases also the resistive torques increase to result in a zero net torque? What is the nature of these resistive torques? Are they frictional torques?

Power= Torque* Angular speed. That said, if the shaft of an engine is connected to another gear that is half the diameter, this second driven gear will start spinning too, i.e. will experience a torque. But the driven will spin at twice the angular speed of the engine and not increase. Why does the speed of the driven gear not increase but remains stable at that fixed value? After all, there is a nonzero torque applied to it...

The second driven gear has a torque that is half the torque that the driving wheel applies to on it. Is this halved, smaller torque a torque that the driven gear can apply to a third gear or is it a torque applied to the driven gear itself?

Iguess a car engine can produce different amounts of mechanical power as it operates at different regimes. Power is energy produced per unit time. For instance, if we floored the accelerator pedal, the RPM would increase and more output power would be produced (the torque would probably decrease as the RPM decrease). There is surely a limit, a maximum power P_max that the engine can produce: that happens for for a certain value of torque and angular speed.

Can that maximum amount of power be produced at any gear when the engine spins at the RPM value? For instance, imagine that the max power speed was 50 RPM. If theengine spun at 50 RPM in first gear or 50 RPM in 2nd gear, would the torque automatically adjust to the right torque to give the max power output? Or does that max power out situation only occur at a specific gear?

thanks,
fog37

 

[SteamKing]

Hello Forum,

If a net nonzero torque is applied to an object that is able to rotate, the object will spin at an increasing angular speed. The torque causes angular acceleration.

In the case of a car engine, the engine eventually spins at a max constant rotational speed omega. Why does the angular speed not continue to increase due to the applied torque? Is it simply because as the speed increases also the resistive torques increase to result in a zero net torque? What is the nature of these resistive torques? Are they frictional torques?

It's because the engine is running under load, and the operator has used the engine throttle to regulate how much power (or torque) the engine is generating. If the load were suddenly removed, like say a car running onto an icy surface, then the loss of load would cause the engine to rev quite suddenly, until the operator adjusted the throttle.

Power= Torque* Angular speed. That said, if the shaft of an engine is connected to another gear that is half the diameter, this second driven gear will start spinning too, i.e. will experience a torque. But the driven will spin at twice the angular speed of the engine and not increase. Why does the speed of the driven gear not increase but remains stable at that fixed value? After all, there is a nonzero torque applied to it...

The second driven gear has a torque that is half the torque that the driving wheel applies to on it. Is this halved, smaller torque a torque that the driven gear can apply to a third gear or is it a torque applied to the driven gear itself?

Again, you operate an engine under some kind of load. If no load is present, then it takes only a small amount of fuel to over speed an engine.

When coupling an engine to a gear, two things happen:

1. the torque output of the engine is multiplied by the gear ratio, and
2. the speed of the output shaft on the gear is the engine speed divided by the gear ratio.

The net effect is that the power coming out of the gear is the same as the power going in, minus a few percent for losses in the bearings, etc.

Iguess a car engine can produce different amounts of mechanical power as it operates at different regimes. Power is energy produced per unit time. For instance, if we floored the accelerator pedal, the RPM would increase and more output power would be produced (the torque would probably decrease as the RPM decrease). There is surely a limit, a maximum power P_max that the engine can produce: that happens for for a certain value of torque and angular speed.

The maximum values of horsepower and torque, and the speeds at which they occur, are reported usually as the 'rated' values for the engine.

Can that maximum amount of power be produced at any gear when the engine spins at the RPM value? For instance, imagine that the max power speed was 50 RPM. If theengine spun at 50 RPM in first gear or 50 RPM in 2nd gear, would the torque automatically adjust to the right torque to give the max power output? Or does that max power out situation only occur at a specific gear?

thanks,
fog37

Now, you're getting mixed up. The engine chugs along, producing the amount of torque which the throttle setting and ambient conditions allow it to produce. This has nothing to do with whatever gears or transmissions the engine is attached to. The purpose of a gear, as described above, is to alter the output speed of the shaft or multiply the amount of torque coming out of the gearbox.

Cars with internal combustion engines require transmissions and differential gears to multiply their torque sufficiently in order to get a car moving initially. The engine cannot produce any torque if it is not turning, and when the car is stopped, the wheels are definitely not turning. So, it takes the momentary application of torque to get the whole contraption going. Less strain is put on the engine by using a gear with a high ratio to magnify the small amount of torque coming out of the engine to get the car rolling. As the car picks up speed, the wheels turn faster and less torque is needed to keep the vehicle in motion, so a gear with a lower ratio is used to match engine speed with the speed of the wheels. This gear ratio also will allow the engine to run at a speed where it is generating the maximum amount of torque, so that the car can get to speed quickly. When the car is cruising, there is no more need to vary the gear ratio to keep the car moving and the speed of the engine matched to the speed of the wheels.

 

[billy_joule]

Hello Forum,
In the case of a car engine, the engine eventually spins at a max constant rotational speed omega. Why does the angular speed not continue to increase due to the applied torque? Is it simply because as the speed increases also the resistive torques increase to result in a zero net torque? What is the nature of these resistive torques? Are they frictional torques?

Almost all modern (injected) cars have rev limiters to prevent damage via overspeed. Most function by stopping the spark plug from firing. Obviously if the plugs aren't firing the engine will slow down.

Older (carb'ed) cars self limit via valve bounce (aka valve float). Above a certain rpm the valves no longer open and close completely, power output is reduced and rpm will become stable. Valve bounce is not good for an engine, rev limiters are generally set to engage just before the onset of valve bounce.

http://en.wikipedia.org/wiki/Valve_float

http://en.wikipedia.org/wiki/Rev_limiter

http://en.wikipedia.org/wiki/Overspeed_(engine)

There are many other ways that an ICE can self limit (eg limited air supply, limited fuel supply etc) but generally valve bounce occurs first.

 

[fog37]

Thank yo SteamKing that was a really good answer.

Let me see if I can summarize some concepts and please correct me wherever I go wrong:

a) the engine has a flywheel that spins at constant RPM (omega1). This angular speed is constant because there is a load (in the form of friction, metal parts to move). When the speed omega1 is reached the net torque is zero (driving torque is canceled by the load torque).

b) The flywheel gets in contact with a smaller diameter gear. The contact could be seen as some sort of collision that slows down the flywheel and speeds up the smaller gear. Eventually the flywheel continues to move at omega1 while the smaller gear at a speed larger than omega1. At the same time, the torque is reduced. What torque are we talking about? Is it the torque exerted on the smaller gear or is it a torque the smaller gear exerts on something else? A torque is something that a force generates when it is applied at a distance from the rotation axis of an object. So each gear in a transmission applies a force to the neighboring gear to make it spin. So we should talk about the torque that each gear exerts on the next. Both the force and the radius of the gear (lever arm) matter.

c) Torque creates acceleration (change in speed) for the car. When the car at rest we need a lot more torque to make it move than when the car is already traveling at a high speed, correct? As the RPMs climb up, the torque should be become smaller.

Thanks,
fog37

 

[SteamKing]

Thank yo SteamKing that was a really good answer.

Let me see if I can summarize some concepts and please correct me wherever I go wrong:

a) the engine has a flywheel that spins at constant RPM (omega1). This angular speed is constant because there is a load (in the form of friction, metal parts to move). When the speed omega1 is reached the net torque is zero (driving torque is canceled by the load torque).

The flywheel is turning at the engine RPM. Except for being toothed around its perimeter to allow the starter motor to spin the engine, that's about all the flywheel does in transmitting power (torque) from the crankshaft to the driving wheels of a car.

b) The flywheel gets in contact with a smaller diameter gear. The contact could be seen as some sort of collision that slows down the flywheel and speeds up the smaller gear.

Here, things are a little more complicated. Let's talk about a car with a manual transmission. An automatic gearbox works in a similar fashion.

A means of disengaging the engine from the transmission is required so that the engine can turn while the car is not moving or when shifting into a different gear. A clutch is used to couple the engine flywheel with the transmission. One part of the clutch is bolted to the flywheel, while the other part is bolted to the input shaft of the transmission. The two parts of the clutch couple the engine to the transmission using friction to transmit the torque of the engine to the gearbox.

Eventually the flywheel continues to move at omega1 while the smaller gear at a speed larger than omega1. At the same time, the torque is reduced.

This is the opposite of what happens. In order to multiply the torque of the engine, the output gear must turn at a slower speed than that of the engine.

As one accelerates and shifts thru the gears of the transmission, the output speed of the transmission more closely matches the engine speed, and the amount of torque multiplication is reduced with each gear change.

What torque are we talking about? Is it the torque exerted on the smaller gear or is it a torque the smaller gear exerts on something else? A torque is something that a force generates when it is applied at a distance from the rotation axis of an object. So each gear in a transmission applies a force to the neighboring gear to make it spin. So we should talk about the torque that each gear exerts on the next. Both the force and the radius of the gear (lever arm) matter.

c) Torque creates acceleration (change in speed) for the car. When the car at rest we need a lot more torque to make it move than when the car is already traveling at a high speed, correct? As the RPMs climb up, the torque should be become smaller.

Once the car is moving, there is no longer a need to multiply the torque produced by the engine. The engine speed and the speed of the drive shaft are the same, but the differential usually contains one final gear which reduces the engine speed one final time to allow the engine to have sufficient torque to turn the wheels to give regular driving speeds without causing the engine to loaf along at too low a speed.
Thanks,
fog37

I think if you watch the video at this link, it will make it easier to understand how these concepts come together in an actual vehicle: