Mirth stands at the center of a very large (diameter 12m) merry-go-round with hi
ID: 1843090 • Letter: M
Question
Mirth stands at the center of a very large (diameter 12m) merry-go-round with his unicycle. His able-bodied assistants have gotten the merry-go-round spinning at a high rate of speed. Dr. Mirth dons his helmet, tells everyone to stand clear, and takes off on a dizzying ride in an attempt to pedal off the merry-go-round without falling over (don't try this at home!). When he reaches a point that is 4.0m from the center, the merry-go-round is spinning ccw at a rate of 2.2 rad/s. with an angular acceleration of 0.6 rad/s^2 in the cw direction. Dr. Mirth's radial velocity is holding steady at 1.3 m/s. At what angle, theta. does Dr. Mirth need to lean forward to maintain his balance? Express your answer in units of degrees.Explanation / Answer
The cyclist is acted upon by two forces. One is centrifugal force and the other is the tangential acceleration due to (=0.6 rad/sec2) . Angle is calculated by equation tan= v2/rg and angle is calculated in the same way that tangential force/mg = tan . We have r=4m, g=9.81 m/sec2, =2.2 rad/sec, =0.6 rad/sec2) calculate v = r = 8.8 m/sec, tan= 8.82/(4x9.81)=1.973 and hence =63.13o and, taking m= mass of the cyclist, tangential force is Ft= mr =2.4m N and the angle tan = tangential force/mg=2.4m/9.81m= 0.249 and hence =14.3o.