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Rotational Kinematics: Kinetic energy of system; weight fallen; angular acceleration

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A 15 kg uniform disk of radius R = 0.25 m has a string wrapped around it, and a m = 5 kg weight is hanging on the string. The system of the weight and disk are initially at rest. When the 5 kg weight is released, it moves down and the disk rotates.

Consider the point when the 5 kg weight is moving with a speed of 1.3 m/s.

a) What is the kinetic energy of the entire system?
b) How far has the weight fallen?
c) What is the angular acceleration of the disk?

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Solution Summary

This solution provides assistance determining the kinetic energy of a system, how far the weight has fallen, and the angular acceleration of the disk.

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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