Solve problems involving motion in a vertical cirlce

Understanding Motion in a Vertical Circle

Grasp the concept of objects moving in vertical circles, including situations where the speed of the object changes such as roller coasters or pendulums.
Understand that gravitational force (mg) also contributes to the total force in vertical circular motion, and consider how this varies depending on the object’s position in the circle.
Recognise the two critical points in vertical circular motion, the bottom point (where speed is at a maximum) and the top point (where speed is at a minimum).
Be familiar with the concept that when the object is at the top of the circle, it must have a minimum speed (v^2 = rg) to continue moving in a circular path, also known as the critical speed.

Begin by identifying all the forces acting on the object at the point of interest in the circular path. This usually includes gravity and the tension or normal force exerted by the constraint.
Use free body diagrams to assist in visualising the forces at play and their directions.
Apply Newton’s second law (F=ma) in the radial direction to establish an equation of motion. Note that acceleration in this context is the centripetal acceleration, ar = v^2/r.
Remember that when considering points at the top or bottom, the gravitational force will either act in the same direction as the centripetal force, or against it.
Be aware that in certain situations, such as objects on strings, the tension can reach zero (at the critical speed) but the object will still continue in circular motion due to its inertia.

Ensure your solutions meet the constraints of the physical problem. For instance, in a string tension problem, the tension cannot be negative.
Review whether the solutions make sense in the context of the problem. For instance, if the calculated speed at the top of the circle exceeds the initial speed, a mistake has likely been made.
Validate your final solutions by substituting them into the original equations to confirm they produce a true statement.

Investigate more complex problems, such as when forces other than gravity and tension come into play.
Develop a deeper understanding of the changes in potential and kinetic energy as objects move in a vertical circle.
Explore real-world applications and see how the principles of vertical circular motion are utilised, such as in the design of roller coasters or in the physics of orbiting satellites.