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
\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}
$$
T = \frac{2 \pi r}{v} = \frac{2 \pi}{\omega}
加速度 (acceleration)
$$
a = r \omega^2 = \frac{v^2}{r}
$$
a = r \omega^2 = \frac{v^2}{r}
$$
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
\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}
\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}
$$
\vec{f} = -m \vec{a}
振動数 (frequency)
$$
f = \frac{1}{T}
$$
f = \frac{1}{T}
$$
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
\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
$$
\omega = \frac{2 \pi}{T} = 2 \pi f
復元力 (restoring force)
\begin{eqnarray*}
F &=& – m \omega^2 x = -Kx \\
\\
T &=& 2 \pi \sqrt{\frac{m}{K}}
\end{eqnarray*}
F &=& – m \omega^2 x = -Kx \\
\\
T &=& 2 \pi \sqrt{\frac{m}{K}}
\end{eqnarray*}
F &=& – m \omega^2 x = -Kx
T &=& 2 \pi \sqrt{\frac{m}{K}}
単振り子 (simple pendulum)
$$
T = 2 \pi \sqrt{\frac{L}{g}}
$$
T = 2 \pi \sqrt{\frac{L}{g}}
$$
T = 2 \pi \sqrt{\frac{L}{g}}