AP Physics Workbook 3.D Vertical Circles

This paragraph introduces the topic of vertical circular motion in AP Physics, focusing on unit three section three point D. The scenario involves a ball (BA) with a weight of two Newtons attached to a chord of length two meters. The tension in the cord is seven Newtons at the top and fifteen Newtons at the bottom. Two students, Dominic and Carlos, discuss the net force on the ball at the top of the circle. Dominic incorrectly assumes the net force is equal to the tension alone, while Carlos correctly identifies that the net force includes both tension and weight. The paragraph clarifies that centripetal force is the resultant of all forces acting towards the center, not a separate force, and that the internal force is a combination of gravitational, normal, tension, and sometimes static frictional forces.

This paragraph delves into the practical application of the physics concepts discussed earlier. It instructs on creating a free body diagram to visualize the forces acting on the ball at different points in its circular path. The paragraph emphasizes the importance of correctly labeling and sizing the vectors to represent the forces accurately. It also touches on the uniform motion of the ball in a clockwise direction and the resultant centripetal force, which is the inward force due to the combination of gravitational and tension forces at the top of the circle.

The paragraph focuses on the mathematical aspect of determining the minimum speed a ball can have at the top of a circular path without leaving it. It explains the derivation of the formula for minimum speed using the given formula sheet and the principles of physics. The explanation includes the substitution of variables and the process of solving for velocity, ultimately leading to the formula that relates gravitational force, velocity, and radius (G = V²/R). The paragraph also provides a practical example problem to illustrate the application of the derived formula.

This paragraph discusses the motion of a ball after the string it was attached to suddenly breaks. It explains the direction the ball will fly based on the instantaneous velocity at the moment of the break, which is tangential to the circle. The paragraph uses Newton's first law to describe the ball's motion as a projectile, detailing the upward trajectory, reaching maximum height, and then falling back down to the ground. It also discusses the changes in velocity during this process, transitioning from positive to zero at the maximum height, and then to negative as the ball descends.

The final paragraph revisits the concepts of centripetal force and projectile motion. It corrects a minor mistake in a previous visual representation, emphasizing the importance of understanding the signs when dealing with the top and bottom of the circular path. The paragraph reinforces the basic vocabulary of centripetal force and provides a comprehensive overview of the physics principles discussed throughout the script.