Solve for question 2The θ integration fails if α is non-constant. There is also a type of situation where the step before the integration fails, involving ω.Question 1: derive ω = αt + ω0.Start with the derivatives I began with, and derive this equation.Question 2: derive θ = 1/2αt2 + ω0t + θ0.You may use prior derived results.Question 3: derive θ = θ0 + (ω + ω0) t/2.You probably need to use prior derived results. The Notion of DerivingDeriving an equation (or a statement) is more than just asserting it. It's showing how it must be true (and anythingcontrary must be false). One doesn't understand the material as long as one is limited to memorizing statements orequations, without being able to connect them.As a further, practical thing, understanding the connection makes it less likely that one would use an equation when itdoesn't apply. In particular, one would avoid the "equations of constant acceleration" anytime one had non-constantacceleration.In this assignment, I assign you to derive the "equations of constant acceleration" -- all but one that I will derive. Wewill use 0, w, and a, satisfying these defınitions:dwandOPαW =dtdtand one special case: a is constant. (You should spot the false step when a is non-constant.) w and 0 are functions oftime: w(t) and O(t). wo = w(0), and 00 = 0(0).My Example: derive w2 - wo² = 2a(0-0).dwdw dodwa =dtde dtdeMultiply by dt and integrate:OPa0 + C =dw =w2= 2a0 + 2CSubstitute the initial (t=0) quantities, and subtract. The constant of integration vanishes.w3 = 2a6, + 2Cw? - wz = 2a(0 – 0o)The 0 integration fails if a is non-constant. There is also a type of situation where the step before the integration fails,involving w.Question 1: derive w = at + wo-Start with the derivatives I began with, and derive this equation.Question 2: derive 0 = 1/2at2 + wot + 0o-%DYou may use prior derived results.Question 3: derive 0Oo + (w + wo) t/2.You probably need to use prior derived results.

we know that, ω=αt+ωo (1) We have to find…

Answered: Question 2: derive θ = 1/2αt2 + ω0t +…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question 1: derive ω = αt + ω₀.

Start with the derivatives I began with, and derive this equation.

Question 2: derive θ = ¹/₂αt² + ω₀t + θ₀.

You may use prior derived results.

Question 3: derive θ = θ₀ + (ω + ω₀)t/2.

You probably need to use prior derived results.

The Notion of Deriving
Deriving an equation (or a statement) is more than just asserting it. It's showing how it must be true (and anything
contrary must be false). One doesn't understand the material as long as one is limited to memorizing statements or
equations, without being able to connect them.
As a further, practical thing, understanding the connection makes it less likely that one would use an equation when it
doesn't apply. In particular, one would avoid the "equations of constant acceleration" anytime one had non-constant
acceleration.
In this assignment, I assign you to derive the "equations of constant acceleration" -- all but one that I will derive. We
will use 0, w, and a, satisfying these defınitions:
dw
and
OP
α
W =
dt
dt
and one special case: a is constant. (You should spot the false step when a is non-constant.) w and 0 are functions of
time: w(t) and O(t). wo = w(0), and 00 = 0(0).
My Example: derive w2 - wo² = 2a(0-0).
dw
dw do
dw
a =
dt
de dt
de
Multiply by dt and integrate:
OP
a0 + C =
dw =
w2
= 2a0 + 2C
Substitute the initial (t=0) quantities, and subtract. The constant of integration vanishes.
w3 = 2a6, + 2C
w? - wz = 2a(0 – 0o)
The 0 integration fails if a is non-constant. There is also a type of situation where the step before the integration fails,
involving w.
Question 1: derive w = at + wo-
Start with the derivatives I began with, and derive this equation.
Question 2: derive 0 = 1/2at2 + wot + 0o-
%D
You may use prior derived results.
Question 3: derive 0
Oo + (w + wo) t/2.
You probably need to use prior derived results.

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