Question $1.[25$ points$]$

A$.[10$ points$]$ The Earth is show in the figure at right. It makes a complete revolution, around its axis, in the course of a day $(24$ hours$).$

a$.$ What is the angular velocity, $\backslash (\backslash$omega $\backslash ),$ of the earth in radians per second?

b$.$ Consider someone living in Chicago, in the northern hemisphere and someone living on the equator.

i$.$ Is the angular velocity, $\backslash (\backslash$omega $\backslash ),$ of the person in Chicago greater than, less than, or equal to the angular velocity of the person on the equator? Explain.

ii$.$ Is the linear velocity, $\backslash (\backslash$boldsymbol$\{$v$\}\backslash ),$ of the person in Chicago greater than, less than, or equal to the linear velocity of the person on the equator? Explain.

B$.[15$ points$]$ A potter's wheel of radius $0\mathrm{.}26$ m is turned on at $\backslash ($ t$=0\backslash )$ and accelerates uniformly. After $72$ s $,$ the wheel has an angular velocity of $\backslash (1\mathrm{.}5\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Show all work.

a$.$ Find the angular acceleration of the wheel.

b$.$ Find the angular velocity of the wheel at $\backslash (\backslash$mathrm$\{$t$\}=50\backslash$mathrm$\{$~s$\}\backslash ).$

c$.$ Find the total angular displacement of the wheel during this time.