EJC Physics H206 Motion in a Circle 2023_1. Notes (FULL)

9749(202 3) H2 Physics H206 Motion In a Circle – Notes Page 1 of 16 H2 Topic 06 – Motion In a Circle We often experience the effects of centripetal (“centre- seeking”) motion on amusement rides. Thrill-seekers can opt for vertical loops in fast roller coasters, while those looking to chill can opt for carousel rides. Content: • Kinematics of uniform circular motion • Centripetal acceleration • Centripetal force Learning Objectives: Candidates should be able to: (a) express angular displacement in radians (b) show an understanding of and use the concept of angular velocity to solve problems. (c) recall and use v = rω to solve problems. (d) describe qualitatively motion in a curved path due to a perpendicular force, and understand the centripetal acceleration in the case of uniform motion in a circle. (e) recall and use centripetal acceleration a = rω2 and a = v2 r to solve problems. (f) recall and use centripetal force F = mrω2 and F = mv2 r to solve problems.

9749(202 3) H2 Physics H206 Motion In a Circle – Notes Page 2 of 16 6.0 Introduction So far, our analysis has been limited to that for linear motion. Here we will work with a simplified view of rotational motion. Nonetheless, we will be able to explain the workings of a centrifuge, the need for inclination of the road on high speed race tracks, the reason behind the thrill -factor of a roller coaster ride, and even the possibility of simulating gravity in space. 6.1 Kinematics of Uniform Circular Motion 6.1.1 Angular Displacement θ Consider an object moving in a typical anti - clockwise circular path of radius r from A to B. Since s rθ = is a ratio, angular displacement θ is technically dimensionless, though we refer to values of angular displacement as having a “unit” of radian: 6.1.2 Angular Velocity ω In an analogous sense, the angular speed of an object is the rate of change of angle (no mention of “displacement”) swept out by a radius.s θ r s A B O Legend s = arc length r = radius (or )s s r r θ θ = = One radian is the angle subtended at the centre of a circle by an arc length that is equal to the radius 1 rad s = r r Angular displacement θ is the angle swept out by a radius. θ : angular displacement (rad) s : arc length (m) r : radius (m) Angular velocity ω is the rate of change of angular displacement swept out by a radius d dt θω = A screen for the read-out of a radar. Quite often seen in popular culture such as movies, the radar readout screen, where a radius sweeps out and reveals “enemies”, is nonetheless a useful image to base your understanding of angular velocity on. ω : angular velocity (rad s−1) d dt θ : rate of angular displacement swept out by radius (rad s−1)

9749(202 3) H2 Physics H206 Motion In a Circle – Notes Page 3 of 16 6.1.3 Uniform Circular Motion Unifo