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Solved: Section 4.7 Nonuniform Circular Motion and Angular
Chapter 4, Problem 31E(choose chapter or problem)
FIGURE EX4.31 shows the angular-velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first \(4 \mathrm{~s}\)?
Equation Transcription:
Text Transcription:
4 s
Questions & Answers
QUESTION:
FIGURE EX4.31 shows the angular-velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first \(4 \mathrm{~s}\)?
Equation Transcription:
Text Transcription:
4 s
ANSWER:Step 1 of 2
We are going to find the revolutions made by the particle which is started from rest.
The initial angular speed \(\omega_{i}=0\)
The angular displacement made by the object is derived using the area (A) under the angular velocity vs time curve given.
From the graph, we need to find the area of the trapezium.
The values of the bases and the height of trapezium up to \(4 \mathrm{~s}\) are given as
The base \(\mathrm{a}=2\) (ins)
The base \(\mathrm{b}=4\) (in s)
The height \(\mathrm{h}=20\) (in \(\mathrm{rad} / \mathrm{s}\) )