HCI 06 Circular Motion Lecture Notes

1 Chapter 6 Circular Motion Image credits to https://en.wikipedia.org/wiki/Singapore_Flyer#/media/File:Singapore_Flyer.JPG The Singapore Flyer is currently one of the tallest Ferris wheel in the world. Described by its operators as an observation wheel, it reaches 42 stories high. At a total height of 165 m (541 feet) and a diameter of 150 m (492.1 feet), it was the tallest Ferris wheel at its inception, 5 m (16 feet) taller than the previous record holder, the Star of Nanchang. The Flyer was itself surpassed in 2014 by the High Roller in Las Vegas, which stands at 167.6 m (550 feet) with a diameter of 158.5 m (520 feet). The Ain Dubai in Dubai which was launched in 2021 stood at a height of 250 m (820 feet). D B C A

2 TOPIC 6: CIRCULAR MOTION Circular Motion Learning Outcomes Students should be able to: Kinematics of uniform circular motion (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) derive, from the definitions of velocity and acceleration, equations which represent uniformly accelerated motion in a straight line. Centripetal acceleration (e) 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. (f) recall and use centripetal acceleration a = rω2, a = v2/r to solve problems. Centripetal force (g) recall and use centripetal force F = mrω2, F = mv2/r to solve problems. Playlist of lecture examples: https://youtube.com/playlist?list=PL_b5cjrUKDlaAYoOvqyWUXVITtqdkKOSO Further Readings / References 1) University Physics with Modern Physics, 14th Ed., Young & Freedman, Chapter 9, Pg 298. 2) Advanced Level Physics, 6th Ed., Nelkon & Parker, Chapter 2, Pg 48. 3) College Physics, 8th Ed., Young & Geller, Chapter 6, Pg 161. 4) Physics for Scientists and Engineers with Modern Physics, 6th Ed., Serway Jewett, Chapter 6, Pg 150.

3 Contents TOPIC 6: CIRCULAR MOTION ................................ .. Error! Bookmark not defined. 6.1 Introduction …………………….…………………………………………………………4 6.2 Kinematics of Circular Motion …………………………………………………………5 6.2.1 How angle is measured ................................ ................................ ................ 5 6.2.2 Angular Displacement (θ) ................................ ................................ .............. 5 6.2.3 Angular Velocity (ω) ................................ ................................ ...................... 6 6.2.4 Relationship between Tangential Speed v and Angular Speed  .................. 6 6.2.5 Period (T) and Frequency (f) ................................ ................................ ......... 7 6.3 Uniform Circular Motion ………………………………………………………………….8 6.3.1 Derivation of the equation of centripetal acceleration .................