60. When you exert a torque on a merry-go-round, how does it exert one on you? I have to exert a lot of torque to get it going but it doesn't feel like torque is being exerted back on me.
When you spin a merry-go-round, you exert a torque on it and it exerts a torque back on you. If you were free to rotate, this torque on you would be quite apparent. Suppose that the merry-go-round was located on an ice skating rink and that you were attached to the central pivot of the merry-go-round by a strap that went around your waist. As you spun the merry-go-round clockwise, you would begin to spin counter-clockwise. In fact, because your moment of inertia is much smaller than that of the merry-go-round, you would experience a much larger angular acceleration and would end up spinning much faster than merry-go-round. The reason that you don't rotate like this after spinning a playground merry-go-round is that your feet touch the ground. As the merry-go-round exerts its torque back on you, you exert that same torque on the ground. The result is that the earth undergoes angular acceleration in the opposite direction from that of the merry-go-round. Because the earth's moment of inertia is so huge, you can't tell that it undergoes angular acceleration at all. It really does, just as the earth undergoes acceleration when you jump-you push down hard and the earth as it pushes up hard on you and you both accelerate away from one another. Since the earth is much more massive than you are, it doesn't accelerate nearly as much as you do.