Wright et al$.(2006)$ studied the elbow range of motion in professional baseball pitchers. They found that the dominant arms had an average flexion angle of $130$ degrees and an extension angle of $5\mathrm{.}5$ degrees. The nondominant arms had an average flexion angle of $135$ degrees and an extension angle of $-2\mathrm{.}4$ degrees $($indicating hyperextension$).$

a$)$ What are the total ranges of motion for the dominant and non$-$dominant elbows? Express your answers in both degrees and radians.

b$)$ During their throwing motion, if a pitcher rotates their forearm about the elbow such that the tangential velocity of the ball is $\backslash (40\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ and the length of the forearm is $28$ cm $,$ what is the angular velocity of the forearm in degrees$/$sec$?$

c$)$ For a pitcher with a forearm that is $1\mathrm{.}5$ cm shorter, how much faster would they need to rotate their forearm to obtain the same baseball tangential velocity $($assume all other factors are equal$)?$