- #1

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## Main Question or Discussion Point

If ##\theta## is angular displacement, does ##\frac{d^2\theta}{dt^2} = (\frac{d\theta}{dt})^2##? Proof?

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- Thread starter Prez Cannady
- Start date

- #1

- 17

- 2

If ##\theta## is angular displacement, does ##\frac{d^2\theta}{dt^2} = (\frac{d\theta}{dt})^2##? Proof?

- #2

- 17

- 2

$$ \theta = sin(t) $$

$$ \frac{d\theta}{dt} = cos(t) $$

$$ \frac{d^2\theta}{dt^2} = -sin(t) $$

$$ \left(\frac{d\theta}{dt}\right)^2 = (cos(t))^2 $$

- #3

olivermsun

Science Advisor

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$$

\begin{align}

\theta(t) &= t \\

\frac{d\theta}{dt} &= 1 \\

\frac{d^2\theta}{dt^2} &= 0 \neq \left( \frac{d\theta}{dt} \right)^2

\end{align}

$$

- #4

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- #5

FactChecker

Science Advisor

Gold Member

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1) If the rotation rate is not changing, the second derivative is zero. Does that mean that it is not rotating at all?

2) Since the right hand side is always positive, does that mean that the rotation rate can only get more positive?

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