Torque & Power: Understanding Angular Velocity

In summary, the conversation discusses the relationship between torque, power, and angular velocity. The speakers question how torque can be equal to both power and the moment of inertia multiplied by the change in angular velocity over time. They also discuss the role of friction in calculating power and how a rotating object at constant velocity can still have a torque. The conversation highlights the importance of understanding equations and the difference between summing torques and the torque itself being zero.
  • #1
firavia
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how can we say that torque is equal to power / angular velocity though we know that torque is equl to I x (change of angular velocity over time ).

and how can we relate torque to (angular velocity) , as we know that a rotating gear at constant angular velocity has no torque on it or bettter saying the sum of all torques on it are equal to zero, so how can we say that torque is equal to the power of the rotating gear over the constant angular velocity ? arent we contradicting ourselfs ?? how can a torque exist on a constant angular velocity rotating gear ? I am confused ??
 
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  • #2
If you push with a force F a block on a table with friction such that the block moves at constant speed v, then the power you produce is Fv. So the conundrum here would be F=ma, but the block is not accelerating? The reason is that we have forgotten to take into account that there is friction. In the presence of friction, if you don't push, the block doesn't even move.
 
  • #3
so u're saying that the torque calculated on the rotating disk is due the force that initialy rotated the disk ?? which means initially accelerated the disk before it reached its equilibriumed state (acceleration = 0) ? right ?
 
  • #4
No, in the example P=Fv, I am giving the constant force (equal and opposite to the friction) you need to apply to keep the block moving at a constant speed.
 
  • #5
firavia said:
how can we say that torque is equal to power / angular velocity though we know that torque is equl to I x (change of angular velocity over time ).
Why do you think these ideas are mutually exclusive? Try writing them in equation form and see if they make more sense.

One thing that may be confusing you - typically that first relationship is written the other way around: power equals torque times angular velocity.
and how can we relate torque to (angular velocity) , as we know that a rotating gear at constant angular velocity has no torque on it or bettter saying the sum of all torques on it are equal to zero, so how can we say that torque is equal to the power of the rotating gear over the constant angular velocity ?
arent we contradicting ourselfs ?? how can a torque exist on a constant angular velocity rotating gear ? I am confused ??
Saying that all torques sum to zero is different from saying that the torque at constant velocity is zero. It is not [necessarily] true to say a rotating object at constant speed has no torque on it: there may an input and an output torque that are equal. Power and energy work the same way.
 

What is torque and how is it related to angular velocity?

Torque is the measure of the force that causes an object to rotate around an axis. It is directly related to angular velocity, as the greater the torque applied to an object, the faster it will rotate.

What units are used to measure torque and angular velocity?

Torque is typically measured in units of Newton-meters (Nm), while angular velocity is measured in units of radians per second (rad/s).

How does the direction of torque affect the rotation of an object?

The direction of torque determines the direction of rotation of an object. If the torque is applied in the same direction as the rotation, it will increase the angular velocity. However, if the torque is applied in the opposite direction, it will decrease the angular velocity.

What is the relationship between power and torque?

Power is the rate at which work is done, and torque is a measure of the force applied to an object. The two are related through the equation P = ω x τ, where P is power, ω is angular velocity, and τ is torque.

How does understanding torque and power help in the design of machines?

Understanding torque and power is crucial in the design of machines because it allows engineers to calculate the necessary torque and power needed for a machine to function properly. This information can also be used to optimize the efficiency and performance of a machine.

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