Solution Found!
Solved: For the equations for I given in parts (a) and (b)
Chapter 9, Problem 15DQ(choose chapter or problem)
A high-speed flywheel in a motor is spinning at \(500 \mathrm{rpm}\) when a power failure suddenly occurs. The flywheel has mass \(40.0 \mathrm{~kg}\) and diameter \(75.0 \mathrm{~cm}\). The power is off for \(30.0 \mathrm{~s}\), and during this time the flywheel slows due to friction in its axle bearings. During the time the power is off, the flywheel makes 200 complete revolutions.
(a) At what rate is the flywheel spinning when the power comes back on?
(b) How long after the beginning of the power failure would it have taken the flywheel to stop if the power had not come back on, and how many revolutions would the wheel have made during this time?
Equation Transcription:
Text Transcription:
500 rpm
40.0 kg
75.0 cm
30.0 s
Questions & Answers
QUESTION:
A high-speed flywheel in a motor is spinning at \(500 \mathrm{rpm}\) when a power failure suddenly occurs. The flywheel has mass \(40.0 \mathrm{~kg}\) and diameter \(75.0 \mathrm{~cm}\). The power is off for \(30.0 \mathrm{~s}\), and during this time the flywheel slows due to friction in its axle bearings. During the time the power is off, the flywheel makes 200 complete revolutions.
(a) At what rate is the flywheel spinning when the power comes back on?
(b) How long after the beginning of the power failure would it have taken the flywheel to stop if the power had not come back on, and how many revolutions would the wheel have made during this time?
Equation Transcription:
Text Transcription:
500 rpm
40.0 kg
75.0 cm
30.0 s
ANSWER:
Solution 15DQ
Introduction
We have to discuss if the formula given for the moment of inertia of rod in the section (a) and (b) of table 9.2.
Step 1
In the derivation of the formula, the thickness was considered to be infinitesimally small. So the shape of the cross section was neglected. Hence, it does not matter whether the cross section is a circle or rectangle, the formula will hold true as long as the thickness is very small compared to its length.
So the cross section need not to be a circle for this formula to be valid.