Average Power Input for Wheel with Rotational Inertia

In summary, a wheel with rotational inertia I and initial speed of 0 is mounted on a fixed motionless axle. The speed of the wheel is then increased to Wf in a time interval T, resulting in a net torque of IWf/T. To find the average power input during this time, the equation P=torque*angular velocity is used. However, this only calculates the power input at one specific time, so the correct method is to find the integral of the power from 0 to T and then divide by T to find the average power input.
  • #1
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Homework Statement


A wheel with rotational inertia I is mounted on a fixed motionless axle. The singular speed w of the wheel is increased from 0 to Wf in a time interval T.
Net torque=IWf/T

What is the average power input to the wheel during this time interval?

Homework Equations


P=torque*angular velocity


The Attempt at a Solution


P=(IWf/T)*Wf=(IWf^2/T)
This isn't right though, what am I doing wrong?
 
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  • #2
Think about this: what's the power input at t = 0? Or at t = T/2? Or generally, at any time between 0 and T? You only calculated the power input at one particular time, but the problem asks for the average.
 
  • #3
I was thinking of finding the integral of the power from 0 to T and then divide everything by T. But for some reason the answer is coming out weird.
 

FAQ: Average Power Input for Wheel with Rotational Inertia

What is average power input for a wheel with rotational inertia?

The average power input for a wheel with rotational inertia is the amount of energy required to keep the wheel turning at a constant speed. It takes into account both the rotational inertia of the wheel and the frictional forces acting on it.

How is average power input calculated for a wheel with rotational inertia?

The average power input for a wheel with rotational inertia can be calculated by dividing the change in energy of the wheel by the time it takes for that change to occur. It can also be calculated by multiplying the torque applied to the wheel by its angular velocity.

Why is understanding average power input important for designing wheels?

Understanding average power input is important for designing wheels because it allows engineers to determine the appropriate amount of torque and speed needed to keep the wheel turning smoothly. This information is crucial for designing efficient and reliable wheel systems.

How does rotational inertia affect average power input for a wheel?

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion. The higher the rotational inertia of a wheel, the more energy is needed to overcome it and maintain a constant speed. This means that a wheel with a higher rotational inertia will require more average power input compared to a wheel with a lower rotational inertia.

Can average power input for a wheel with rotational inertia be reduced?

Yes, average power input for a wheel with rotational inertia can be reduced by reducing the rotational inertia of the wheel or by decreasing the frictional forces acting on it. This can be achieved through design modifications such as using lighter materials, improving the wheel's aerodynamics, or using lubricants to reduce friction. Additionally, using a more efficient power source can also help reduce the average power input needed for a wheel with rotational inertia.

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