Can these please be solved on paper with a step by step explanation please Answers: 4) a. 13.4 s b. 4.28 m/s5) 1/3 ML^26) 421/30 ML^27) 177 N

4) Mike is riding his unicycle of wheel diameter 20 in. Mike rides for 30 m with an initial angular velocity of 0.75 rad/s and an acceleration of 1.2 rad/s?. (a) How long does it take to ride the 30 m? (b) What is the unicycle's linear velocity at 30 m? 5) Derive the equation for the moment of inertia of a one dimensional stick of mass M and length L about an axis perpendicular to the stick through one end. 6) What is the moment of y-axis inertia about the y-axis for the system as shown. The stick has a length of 2L and a mass of M. The solid sphere has a diameter of L and a mass of 2M. 7) A merry-go-round of mass 150 kg and radius 1.5 m is set in motion by a rope that has been wrapped around it. Calculate the constant force that you would have to apply to the rope in order for the merry-go-round to start from rest and achieve and angular velocity of 0.5 rev/s in 2 s