in horizontal plane. Assuming the merry$-$go$-$round is a uniform disk find its angular momentum and kinetic energy.

$5.$ Which has greater angular momentum: a solid sphere of mass $m$ rotating at a constant angular frequency ${}_0$ about the $z-$axis, or a solid cylinder of same mass and rotation rate about the $z-$axis? $(1)$

$6.$ An artificial satellite is placed into an elliptical orbit about the earth, as illustrated in Figure. Telemetry data indicate that its point of closest approach $($called the perigee$)$ is $r_p=8\mathrm{.}37{10}^6$ m from the center of the earth, and its point of greatest distance $($called the apogee$)$ is $r_{A}25\mathrm{.}1{10}^{6}m$ from the center of the earth. The speed of the satellite at the perigee is $v_p=8450\frac{m}{s}.$ Find its speed $v_A$ at the apogee.

$(3$