$(1)\cdot (2)$ $(a)$ 日本語表記: 速度，英語表記: velocity $(b)$ 日本語表記: 加速度，英語表記: acceleration $(3)$ \[\begin{align} x &=R\cdot \cos\theta + L\cdot \cos\phi\\ &=R\left(\cos\theta + \frac{L}{R}\cos\phi \right) \end{align}\] \[ R\cdot \sin\theta = L\cdot \sin\phi \ より \ \sin\phi=\frac{R}{L}\sin\theta\\ \] \[\begin{align} \cos\phi &=\sqrt{1-\sin^2\phi} \\ &=\sqrt{1-\left(\frac{R}{L}\right)^2 \sin^2\theta}\\ &\fallingdotseq1-\frac{1}{2}\left(\frac{R}{L} \right)^2 \sin\theta \end{align}\] \[ よって、x=R \left[ \cos\theta +\frac{L}{R}\left\{1-\frac{1}{2} \left(\frac{R}{L} \right)^2 \right\}\sin^2\theta \right] \] \[ \therefore x=R \left( \cos\theta +\frac{L}{R}-\frac{1}{2}\cdot\frac{R}{L}\sin^2\theta \right) \] $(4)$ \[\begin{align} \frac{dx}{dt} &=\frac{d}{dt}\left\{R\left(\cos\theta +\frac{L}{R} - \frac{1}{2}\cdot \frac{R}{L} \cdot \sin^2\theta \right) \right\} \end{align}\] \[\sin^2\theta=\frac{1}{2}\left(1-\cos2\theta\right) \ より、\] \[\begin{align} &=\frac{d}{dt}\left\{R\left(\cos\theta +\frac{L}{R} - \frac{1}{2}\cdot \frac{R}{L} \cdot \frac{1}{2}\cdot \left(1-\cos2\theta\right) \right) \right\}\\ \end{align}\] \[ \theta = \omega t より、 \] \[\begin{align} &=\frac{d}{dt}\left[R\left\{\cos\omega t +\frac{L}{R} - \frac{1}{2}\cdot \frac{R}{L} \cdot \frac{1}{2} \left(1-\cos2\omega t \right)\right\} \right]\\ &=R \left\{-\omega \cdot \sin\omega t -\frac{1}{4}\cdot \frac{R}{L}\left(2\omega \cdot \sin2\omega t \right)\right\} \end{align} \] \[ \therefore v=-R\omega \left(\sin\omega t +\frac{1}{2}\cdot \frac{R}{L} \cdot \sin2\omega t \right) \] $(5)$ \[\begin{align} \frac{dv}{dt} &=\frac{d}{dt}\left\{-R\omega \left(\sin\omega t +\frac{1}{2}\cdot \frac{R}{L} \cdot \sin2\omega t \right)\right\}\\ &=-R\omega \left(\omega \cdot \cos\omega t +\frac{1}{2}\cdot \frac{R}{L}2\omega \cdot \cos2\omega t \right) \end{align}\] \[ \therefore a =-R\omega^2 \left(\cos\omega t + \frac{R}{L} \cdot \cos2\omega t \right) \] $(6)$ \[\begin{align} v &=-50\,\rm{mm}\times 100\,\rm{rad/s}\left(\sin45^\circ +\frac{1}{2}\cdot \frac{50\,\rm{mm}}{200\,\rm{mm}}\cdot \sin\left(2\times45^\circ \right) \right) \\ &=-4160\ \rm{mm/s} \end{align}\] \[ \therefore v=-4.16\ \rm{m/s} \] \[\begin{align} a &=-50\,\rm{mm}\times \left( 100\,\rm{rad/s} \right)^2\left(\cos45^\circ + \frac{50\,\rm{mm}}{200\,\rm{mm}}\cdot \cos\left(2\times45^\circ \right) \right) \\ &=-3.535\times10^5\ \rm{mm/s^2} \end{align}\] \[ \therefore a =-354\ \rm{m/s^2} \]