高校物理 力学 ~ 円運動と単振動

角速度 (angular verocity)

\begin{eqnarray*}
\omega = \frac{\theta}{t} \\
\\
\theta = \omega t \\
\\
v = r \omega
\end{eqnarray*}
\omega = \frac{\theta}{t}

\theta = \omega t

v = r \omega

周期 (period)

$$
T = \frac{2 \pi r}{v} = \frac{2 \pi}{\omega}
$$
T = \frac{2 \pi r}{v} = \frac{2 \pi}{\omega}

加速度 (acceleration)

$$
a = r \omega^2 = \frac{v^2}{r}
$$
a = r \omega^2 = \frac{v^2}{r}

向心力 (centripetal)

\begin{eqnarray*}
m r \omega^2 = F \\
\\
m \frac{v^2}{r} = F
\end{eqnarray*}
m r \omega^2 = F

m \frac{v^2}{r} = F

遠心力 (centrifugal force)

\begin{eqnarray*}
f = m r \omega^2 \\
\\
f = m \frac{v^2}{r}
\end{eqnarray*}
f = m r \omega^2

f = m \frac{v^2}{r}

慣性力 (inertial force)

$$
\vec{f} = -m \vec{a}
$$
\vec{f} = -m \vec{a}

振動数 (frequency)

$$
f = \frac{1}{T}
$$
f = \frac{1}{T}

単振動の変位・速度・加速度

\begin{eqnarray*}
x &=& A \sin \theta = A \sin \omega t \\
\\
v &=& A \omega \cos \omega t \\
\\
a &=& – A \omega^2 \sin \omega t = – \omega^2 x
\end{eqnarray*}
x &=& A \sin \theta = A \sin \omega t

v &=& A \omega \cos \omega t

a &=& – A \omega^2 \sin \omega t = – \omega^2 x

角振動数 (angular frequency)

$$
\omega = \frac{2 \pi}{T} = 2 \pi f
$$
\omega = \frac{2 \pi}{T} = 2 \pi f

復元力 (restoring force)

\begin{eqnarray*}
F &=& – m \omega^2 x = -Kx \\
\\
T &=& 2 \pi \sqrt{\frac{m}{K}}
\end{eqnarray*}
F &=& – m \omega^2 x = -Kx

T &=& 2 \pi \sqrt{\frac{m}{K}}

単振り子 (simple pendulum)

$$
T = 2 \pi \sqrt{\frac{L}{g}}
$$
T = 2 \pi \sqrt{\frac{L}{g}}