mass M is at rest m is doing circular motion around center o2 r and angle Theta are known  draw a free-body diagram for both M and m.  list the force equations for the rotation mass m, horizontal direction x and vertical direction y, and force equation M find the time for m to complete one period

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Newton’s Third Law of Motion

The horse pulls the cart and the cart pulls the horse in response as per Newton third law. So the big question is, “Don’t the two forces cancel each other? How does the cart accelerate?”