RI Chap 7 Circular Motion Lecture Notes

7 CIRCULAR MOTION H2 Physics 9478 Content Page 7.1 Introduction 2 7.2 Kinematics of Uniform Circular Motion 3 7.3 Dynamics of Uniform Circular Motion 7 7.4 Problem Solving Strategy for Uniform Circular Motion 11 7.5 Uniform Horizontal Circular Motion 11 7.6 Vertical Circular Motion 16 Learning Outcomes Candidates should be able to: (a) express angular displacement in radians. (b) show an understanding of and use the concept of angular velocity. (c) recall and use vr ω= to solve problems. (d) show an understanding of centripetal acceleration in the case of uniform motion in a circle, and qualitatively describe motion in a curved path (arc) as due to a resultant force that is both perpendicular to the motion and centripetal in direction. (e) recall and use centripetal acceleration 2ar ω= and 2avr= to solve problems. (f) recall and use 2F mr ω= and 2F mv r= to solve problems.

Page | 2 7.1 Introduction Circular motion is a common occurrence in our daily lives. The second hand of a clock goes round in a circle in 60 seconds while the Earth orbits the Sun once in 365 days. You probably have also experienced circular motion when you sat on a carousel or in the Singapore Flyer. As physics students, you want to go beyond the physical experience. You want to understand what causes an object to move in a circular motion and the physical quantities associated with it. For a body moving in a circular path, it must already be travelling with a certain linear speed and at the same time, there must be a force applied on it that is directed towards the centre of the circular path. As the body tries to move off in a straight line, the applied force towards the centre pulls the body inwards, causing it to move in a curve. The continuous application of this centre- pointing force allows the body to move in a circular path. This force is aptly given the name centripetal force wher e “centri” means centre and “petal” means pointing in Latin. The H2 Physics syllabus classifies circular motion into two categories: uniform and non-uniform circular motion. Uniform circular motion can be described as the motion of a body in a circle at a constant speed. As the body moves in a circle, it is continuously changing its direction. At all instances, the body ’s velocity is tangent to the circle. For the magnitude of the velocity (speed) to remain constant, the resultant force on the body must continuously act perpendicular to it s velocity . Hence the resultant force only has a centripetal component which points radially towards the centre of the circular path, with no component in the tangential direction. In a non-uniform circular motion, the speed of the body is varying. This occurs when the resultant force on the body has both centripetal (radial) and tangential component s. The tangential component of the resultant force causes the speed to vary. The centripetal component continuously changes the