Solution Found!
Unless otherwise stated, in the following
Chapter 3, Problem 17E(choose chapter or problem)
Unless otherwise stated, in the following problems we assume that the gravitational force is constant with \(g=9.81\ m/sec^{2}\) in the MKS system and \(g=32\ ft/sec^{2}\) in the U.S. Customary System.
In Problem 16, let \(I=50\ \text {kg-}\mathrm{m}^{2\) and the retarding torque be \(5 \sqrt{\omega}\ \text {N-m}\). If the motor is turned off with the angular velocity at \(225\ \mathrm{rad} / \mathrm{sec}\), determine how long it will take for the flywheel to come to rest.
Equation Transcription:
Text Transcription:
g=9.81 m/sec^{2}
g=32 ft/sec^{2}
I=50kg-{m}^{2
5 sqrt{omega} {N-m}
225 rad/sec
Questions & Answers
QUESTION:
Unless otherwise stated, in the following problems we assume that the gravitational force is constant with \(g=9.81\ m/sec^{2}\) in the MKS system and \(g=32\ ft/sec^{2}\) in the U.S. Customary System.
In Problem 16, let \(I=50\ \text {kg-}\mathrm{m}^{2\) and the retarding torque be \(5 \sqrt{\omega}\ \text {N-m}\). If the motor is turned off with the angular velocity at \(225\ \mathrm{rad} / \mathrm{sec}\), determine how long it will take for the flywheel to come to rest.
Equation Transcription:
Text Transcription:
g=9.81 m/sec^{2}
g=32 ft/sec^{2}
I=50kg-{m}^{2
5 sqrt{omega} {N-m}
225 rad/sec
ANSWER:Solution:
Step 1:
In this problem we need to find the time when the flywheel to come to rest.
Let us consider, the angular velocity is .
Torque from the motor is T.
The moment of inertia of flywheel is .
Initial angular velocity of the flywheel is .
Retarding torque due to friction is proportional to the angular velocity
.
That is, , where k is the proportional constant.
By newton’s second law for rotation of motion we have:.
That is,
Therefore,