Consider the case of a rotating wheel at rest and starting a

sunshine022uv 2021-12-18 Answered

Consider the case of a rotating wheel at rest and starting a clockwise rotation, meaning the negative direction of the angular velocity, and increasing (negatively) its value up to 12radsec for 2 seconds. It then maintains a constant velocity for 2 seconds, and then uniformly reduces the magnitude of the velocity for 2 seconds until the wheel is momentarily stopped and restarts its rotation counter clockwise with positive angular velocity, accelerating up to 20radsec in 2 seconds and remaining at a constant rotation for 2 more seconds. Finally, the wheel stops gradually in 2 seconds. Next you can see the graph of angular velocity versus time of this rotation:
Slope:Origin intercept:Equation:ω=f(t)
image

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Expert Answer

ambarakaq8
Answered 2021-12-19 Author has 31 answers

Step 1
The graph in the interval [0, 2] is a straight line
The standard equation of a line in slope intercept form is y=mx+c where m is the slope of the line and c is the y-intercept.
The horizontal axis is x-axis and vertical axis is y-axis.
Step 2
The two points from which slope will be calculated are:
(0, 0) and (2, 12)
which are the respective endpoints of the line.
Calculate the slope.
m=y2y1x2x1
=12020
=6
Hence the slope is -6.
The y-intercept is the point where the line intersects the y-axis. This point is clearly the origin. Hence the origin y-intercept is 0 since the y-coordinate at this point is 0.
The y-axis is represented by ω and the x-axis is represented by
The equation of the line is thus framed.
ω=mt+c
ω=6t+0
Hence the equation of the line is ω=6t

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usaho4w
Answered 2021-12-20 Author has 39 answers

Let us derive the formula to find the value of the slope if two points
(x1, y1) and (x2, y2)
on the straight line are known. Then we have
y1=mx1+b
and y2=mx2+b
We know that, slope=change in ychange in x
Substituting the values of y1 and a2, we get
y2y1x2x1=(mx2+b)(mx1+b)x2x1
=mx2mx1x2x1
=m(x2x1)x2x1
=m
Thus we find that the slope (m) is calculated as (change in y)(change in x)
m=difference in y coordinatesdifference in x coordinates

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