Problem $22\mathrm{.}1\mathrm{.}5$

How many degrees of freedom is the system shown in Fig. $22\mathrm{.}6\mathrm{.}5?$ Use the Newton $-$ Euler method to write the equation$($s$).$ Hint: be careful with the relationship between the direction of motion of the mass and the sign of the rotation angle.

$22\mathrm{.}5$ More Examples

$99$

Figure $22\mathrm{.}6\mathrm{.}5$: The axel of a rolling wheel on a non$-$slipping surface is connected to a spring and an inextensible cable, which in turn is connected to a mass after being redirected by a pulley. Assume the wheel is a solid disk with uniform mass distribution and that the pulley that redirects the cable is massless.