Uniform Circular Motion Free Body Diagrams

This paragraph delves into the concept of uniform circular motion, emphasizing that while the speed is constant, the velocity changes due to its changing direction. The velocity vector is always tangent to the circle, and the acceleration vector points directly towards the center, perpendicular to the velocity. This is because the object is not speeding up or slowing down but merely changing direction. The net force and acceleration are always directed towards the center of the circle, defining uniform circular motion. Centripetal force and centripetal acceleration are introduced as the inward force and acceleration towards the center, contrasting with the misconception of centrifugal force.

The second paragraph illustrates how to draw Free Body Diagrams (FBD) for objects in uniform circular motion, using examples such as a car tethered by a string and a person on a merry-go-round. It explains that the centripetal force, which keeps the object moving in a circle, can be identified by considering the unbalanced forces acting towards the center. For the car, the tension in the string provides the centripetal force, while for the person on the merry-go-round, it's the force exerted by the railing or their hand. The paragraph encourages viewers to visualize the forces and FBDs for different scenarios.

This paragraph explores the role of friction as a centripetal force in various situations, such as standing on a rotating platform without railings or driving a car in a circular path. It clarifies the difference between static and kinetic friction, noting that static friction is responsible for keeping an object in place during circular motion. The paragraph also discusses the potential dangers of reduced friction, such as on an icy road, which can lead to a loss of the centripetal force and a straight-line motion away from the circular path.

The fourth paragraph discusses the forces involved in amusement park rides, such as the mineshaft ride, where participants are pressed against a wall due to the centripetal force provided by the normal force and static friction. It explains how the normal force increases as the ride spins faster, which in turn increases the maximum static friction that prevents sliding. The paragraph highlights the importance of these forces in maintaining circular motion and the consequences of their absence, such as in the case of the mineshaft ride being discontinued due to safety concerns.

This paragraph examines the forces acting on a ball swinging in an arc and how to calculate the centripetal force in such scenarios. It explains that the tension in the string and gravity act on the ball, and for uniform circular motion, the tension must be greater than gravity to provide the necessary centripetal force. The paragraph also discusses how changing the tension affects the ball's position in the swing, with increased tension causing the ball to move higher until the forces balance out again.

The sixth paragraph analyzes the forces acting on a roller coaster cart as it moves through different parts of a circular track. It explains how the normal force and gravity interact to provide the centripetal force needed for circular motion. At the bottom of the loop, the normal force must be greater than gravity to push the cart upwards, while at the top, gravity provides the downward centripetal force as the normal force decreases. The paragraph emphasizes the importance of the net force towards the center for maintaining circular motion.