Uniform Circular Motion Overview

Overview

This lecture introduces uniform circular motion, explaining the key concepts of tangential speed, centripetal acceleration, and centripetal force, while clarifying common misconceptions about centrifugal force.

Uniform Circular Motion Basics

• Uniform circular motion occurs when an object moves in a circle at constant tangential speed.
• Objects exhibit circular motion when they revolve around a fixed axis with a constant radius.
• Tangential speed is the speed of an object along the tangent to its circular path at any instant.

Tangential Speed and Radius

• Tangential speed depends on how far the object is from the axis of rotation; farther objects move faster.
• Objects closer to the center travel less distance in the same time, resulting in slower tangential speed.

Centripetal Acceleration

• Centripetal acceleration always points toward the center of the circle.
• Even when speed is constant, the changing direction of velocity means there is always acceleration toward the center.
• Formula: Centripetal acceleration = (tangential speed)² / radius.

Centripetal Force

• Centripetal acceleration requires a force toward the center, called the centripetal force.
• Formula: Centripetal force = mass × centripetal acceleration = m(v²/r).
• Examples include tension, gravity, or friction depending on the system.
• If centripetal force vanishes, the object moves in a straight line tangent to the circle at the release point.

Centrifugal "Force" and Inertia

• The outward "centrifugal force" is not a real force, but a feeling due to inertia (Newton's first law).
• Inertia makes your body want to continue in a straight line when the actual force pulls you inward.

Key Terms & Definitions

• Uniform circular motion — motion along a circular path at constant speed.
• Tangential speed — speed along the tangent to the circle at any point.
• Centripetal acceleration — acceleration directed inward, keeping an object moving in a circle.
• Centripetal force — force causing centripetal acceleration, always directed toward the center.
• Inertia — tendency of an object to resist changes in its motion.
• Centrifugal force — perceived outward force in circular motion; not a true force.

Action Items / Next Steps

• Review examples and practice calculating centripetal acceleration and force using provided formulas.