# Why doesnt net torque cause angular velocity to increase upto infinity?

• ashutoshd
In summary, the angular velocity of a shaft will continue to increase until the resisting torque equals the driving torque. This is why motors and engines are designed with systems to limit their speed. Additionally, the stresses on a spinning object increase exponentially with RPM, so there is a physical limit to how fast an object can safely spin before it fails. In a motor, if the RPM exceeds the rotation speed of the magnetic field, a negative torque acts as a break on the motor. This is also why motors can act as generators when their RPM exceeds the synchronized velocity.
ashutoshd
If i have a shaft & I'm applying a driving torque D at one end & at other end there is resisting torque R due to bearing friction, etc. Then if D>R, i have net torque = moment of inertia times angular acceleration. Since the ang. accln is constant with respect to time, will the ang. speed of shaft keep increasing till infinity? If the answer is yes, then why doesn't this happen to motors & engines @ low or no load? Another doubt is that by conservation of energy we have input power= output power + losses, so if i am giving finite input power, the output power has to be finite. Since rotational kinetic energy of shaft is half * MI * square of angular velocity, angular velocity cannot be infinite as that would make output power infinite, right? Please help this is so confusing

Generally, the resisting torque R increases as angular velocity does, until D=R and the stationary state is reached

In motors, as the angular velocity approaches the synchronized velocity, which depends on the frequency of the electric power and also on the number of poles in the winding, the torque decrease. in absolute no-lode, the torque becomes zero. This happens because when the rotor is rotating with the same speed as the magnetic field is rotating, no current is induced in the rotor.

For engines also there is a system to reduce the fuel to keep the speed low, unless you press the gas pedal.

Also the motor torque tends to decrease as speed increases. Note, that may not be true for low speeds with some types of motor (e.g. a car gasoline or diesel engine), but it will be true when the speed gets high enough, because any real motor can only deliver a limited amount of power, and power = torque x RPM.

The ideal-world answer is that the rpm wouldn't increase to infinity (as we're limited by the speed of light), but would indeed continue increasing to a high level IF we can continue applying the torque.

Realistically we either can't keep up with it for the various mentioned reasons, or, perhaps more likely, we are simply limited by the mechanical strength of the spinning object. Stresses due to spinning increase as a function of RPM2, so they get very high very fast. The limit to how fast you can safely spin is the redline, which is usually kept from being exceeded by a mechanical or electronic governor.

If the redline DOES get exceeded, the spinning object, such as a motor, can fail catastrophically.

Don't ask me how I know :(

In a motor, if the rpm exceeds the rotation speed of the magnetic field, the shaft experiences a negative torque which acts like a break on the motor. Of course the motor would be acting like a generator then.

## 1. Why doesn't net torque cause angular velocity to increase indefinitely?

Net torque is a measure of the total force applied to an object that causes it to rotate. It is not the only factor that determines the angular velocity of an object. Other factors such as the moment of inertia and the object's mass also play a significant role in determining the final angular velocity. Therefore, even with a high net torque, the angular velocity will eventually reach a maximum value due to these other factors.

## 2. How does angular velocity relate to net torque?

Angular velocity is directly proportional to the net torque applied to an object. This means that an increase in net torque will result in an increase in angular velocity, and a decrease in net torque will result in a decrease in angular velocity.

## 3. Can an object have a net torque but no angular velocity?

Yes, an object can have a net torque without any angular velocity. This can happen if the object is at rest or if it is in a state of equilibrium, where the net torque is balanced by an equal and opposite torque.

## 4. What happens to net torque and angular velocity when an object is in motion?

When an object is in motion, its angular velocity can change due to changes in net torque. If the net torque remains constant, the object will continue to rotate at a constant angular velocity. Any change in the net torque will result in a change in the angular velocity, either increasing or decreasing it.

## 5. Can net torque be negative?

Yes, net torque can be either positive or negative. Positive net torque causes an object to rotate in a counterclockwise direction, while negative net torque causes it to rotate in a clockwise direction. The direction of the net torque is determined by the direction of the force and the distance from the axis of rotation.

• Mechanics
Replies
16
Views
2K
• Mechanics
Replies
8
Views
2K
• Introductory Physics Homework Help
Replies
32
Views
1K
• Mechanics
Replies
4
Views
3K
• Mechanics
Replies
22
Views
2K
• Mechanical Engineering
Replies
2
Views
2K
• Mechanics
Replies
2
Views
1K
• Mechanics
Replies
6
Views
3K
• Mechanical Engineering
Replies
4
Views
4K
• Mechanics
Replies
1
Views
2K