Torque on a rotating disk: calculate torque exerted by friction and rotational friction work.

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Torque on a rotating disk: calculate torque exerted by friction and rotational friction work.
We are given the specifications on a heavy rotating disk, and the first order of business is to convert the rotational speed from RPM to radians per second.
In the first question, we are asked to calculate the torque exerted by friction as the disk slows to a stop. To get this done, we apply the rotational equivalent of Newton's second law: tau=I*alpha. We use the standard geometric formula for the moment of inertia of a disk: 1/2*M*R^2, and we compute the average angular acceleration using delta(omega)/delta(t). Multiplying moment of inertia and angular acceleration, we obtain the average torque exerted on the disk by friction.
In the second question, we are asked for the work done by friction as the disk slows to a stop. We compute this work by looking at the initial kinetic energy of the disk, and we realize the work done by friction is simply the negative of this quantity, since friction is responsible for removing the energy from the system. We compute the rotational kinetic energy using 1/2*I*omega^2, and we've got the work done by friction on the rotating disk.

[@ptyptypty3]

absolutely EXCELLENT!! thank you for a perfect VIDEO on this type of Problem...

[@ZaksLab]

I'm glad I could help! -z

[@jamie-lynngoulter2494]

This was amazing thank you

[@ZaksLab]

you're welcome! z

[@nightstalker7661]

is the formula T=Force x radius can be used here, say we need to find the force needed to rotate the disk?

[@ZaksLab]

You would have to know the radius at which the force is applied, which isn't clear from the problem (maybe the force is due to friction in a small bearing at the center?) . There are variants of the problem where the radius is known, for example slowing a disk by pressing a piece of metal against the outer edge and using friction to exert a torque. Then the radius would be the radius of the disk.

[@chasekersteinstudent]

torque should be negative here, no?

[@ZaksLab]

If you call the direction of initial angular velocity positive, then torque would be negative if we were to use the sign to indicate direction. That choice of "which way is positive" is arbitrary though, which is why I chose to just compute the magnitude of the torque. If you wanted to use the result to do an angular kinematics problem you'd have to choose a direction to call positive and be consistent after that choice (if omega_0 is positive, then alpha is negative or vice versa). z

[@chasekersteinstudent]

@@ZaksLab perfect, thanks for the quick reply!

[@anengineer8647]

Hiii I hv doubt in torque cal.... what if we don't have time ..how to calculate alpha

[@ZaksLab]

The time to slow to a stop depends on the torque! If time is smaller, alpha is larger and the torque is larger; if time is larger, alpha is smaller and the torque is smaller.

[@anengineer8647]

@@ZaksLab ok understand but in actual conditions we don't have stoping time.. can you share me your email id I want to share my problem sheet with you ..that will be very helpful

[@ZaksLab]

@@anengineer8647 click on my channel then "About", then you should see a tab to get my email

[@anengineer8647]

@@ZaksLab sir I checked but unable to find it please share

[@anengineer8647]

@@ZaksLab I will mail you my sheet