Circular Motion Concepts

Overview

This lecture covers the core concepts, formulas, and definitions related to motion in a circle, including angular measurements, kinematics, centripetal acceleration, and centripetal force for CAIE Physics A-level.

Kinematics of Uniform Circular Motion

• Angles are measured in radians; one radian is the angle when arc length equals the radius.
• A complete circle is (2\pi) radians, which is (360^\circ).
• Convert degrees to radians by multiplying by (\pi/180); radians to degrees by multiplying by (180/\pi).
• Angular displacement ((\theta)) is the angle turned through in radians.
• Angular speed ((\omega)) is the angle moved through per unit time ((\omega = \theta/t)).
• Angular speed can also be found by (\omega = v/r) or (\omega = 2\pi/T), where (T) is the period.
• Linear speed ((v)) is given by (v = r\omega).

Centripetal Acceleration and Centripetal Force

• An object moving in a circle at constant speed accelerates since its velocity direction changes.
• Centripetal force is required for circular motion and always acts toward the center.
• Centripetal acceleration, (a), is given by (a = v^2/r) or (a = r\omega^2).
• Centripetal force, (F), is given by (F = mv^2/r) or (F = mr\omega^2), where (m) is mass.

Key Terms & Definitions

• Radian — Angle where arc length equals the radius; (2\pi) radians in a circle.
• Angular displacement ((\theta)) — Angle an object turns through, measured in radians.
• Angular speed ((\omega)) — Rate of change of angular displacement, in radians per second.
• Linear speed ((v)) — Speed along the circular path, calculated by (v = r\omega).
• Centripetal acceleration ((a)) — Acceleration toward the center required for circular motion ((a = v^2/r)).
• Centripetal force ((F)) — Force acting toward the center that keeps an object moving in a circle ((F = mv^2/r)).

Action Items / Next Steps

• Practice converting between degrees and radians.
• Review and memorize the formulas for angular speed, linear speed, centripetal acceleration, and force.
• Complete all assigned problems on circular motion.