7) A cockroach rides the rim of a rotating merry-go-round. If the angular speed of this system(merry-go-round + cockroach) is constant, does the cockroach have (a) radial accelerationand (b) tangential acceleration? If w is decreasing, does the cockroach have (c) radialacceleration and (d) tangential acceleration?8) The figure shows three small spheres that rotate about a vertical axis. Theperpendicular distance between the axis and the center of each sphere is given. Rankthe three spheres according to their rotational inertia about that axis, greatest first.1m 36 kg2 mRotationaxis3 m09 kg4 kg

Disclaimer: “Since you have asked multiple question, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question.” Disclaimer: “Since you have asked posted a question with multiple sub-parts, we will solve the first three sub-parts for you. To get remaining sub-part solved please repost the complete question and mention the sub parts to be solved.” We are given a cockroach sitting on rim of merry go round. Hence the cockroach goes circular motion. For first case, the angular velocity is constant. For other case, this angular velocity is decreasing. We discuss about tangential and radial acceleration for both cases.Part a) Initially the angular velocity ω=constant. Let the radius of rim be r which is the radius of circular motion for cockroach. Since the direction of velocity for cockroach is changing, this means that there is radial acceleration given as ac=ω2r Hence the cockroach has radial acceleration which is constant. Part b) The tangential acceleration is given as at=rα Here α=dω/dt is angular acceleration. Since angular velocity is constant, there is no angular acceleration. Hence, there is no tangential acceleration. Part c) Now the angular velocity is decreasing. The cockroach is still in circular motion meaning that direction of motion is changing meaning there is radial acceleration. This is given as ac=ω2r Here ω is instantaneous angular velocity at ant time. Hence there is radial acceleration.

Answered: 7) A cockroach rides the rim of a…