DHS 06 Motion in a Circle (Lecture Notes & Tutorial)

Dunman High School (Senior High Physics Department) 9749 Physics (2024) Topic 6: Motion in a Circle Topic 6 - Student Notes - Page 1 Guiding Questions  How do we describe the motion of an object moving in a circular path?  What causes an object to move in a circular path? Content  Kinematics of uniform circular motion  Centripetal acceleration  Centripetal force 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 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 H2 Physics Topic 6 Motion in a Circle Year 5 (2024) DUNMAN HIGH SCHOOL

Dunman High School (Senior High Physics Department) 9749 Physics (2024) Topic 6: Motion in a Circle Topic 6 - Student Notes - Page 2 6.1 Circular Motion: An Introduction (a) express angular displacement in radians. So far, we have discussed the motion of an object in a straight line (linear motion) and a parabolic path (projectile motion). However, in real life, there are many cases of objects moving in an arc of a circle or a circular path. For example, we can tie a ball to a string and swing it in a horizontal circle. Suppose the radius of this circle is r and the ball travels a distance (arc length) of s, its angular displacement will be θ. Angle θ in radians is the ratio of the distance s along a circular arc subtended by θ divided by the radius r. s r θ= If s = r, then θ =1 radian. Since circumference of circle ,diameter of circle  the circumference of a circle = 2πr. So for one revolution 2 .2 2 s r r r     θ= o o o 2 radian 360 360Thus, 1 radian 57.32      Conversion to degree can be done using: o (rad) 180      Translate degrees to radians: degrees180 180 Translate radians to degrees: r adians      One radian is

Dunman High School (Senior High Physics Department) 9749 Physics (2024) Topic 6: Motion in a Circle Topic 6 - Student Notes - Page 3 6.1.1 Angular velocity ω (b) show an understanding of and use the concept of angular velocity to solve problems. Angular velocity, ω, is the rate of change of angular displacement. = d dt  Its unit is rad s−1. When the angular velocity is constant, t   angle moved through in time time taken t the body is then said to be undergoing uniform circular motion, i.e. the motion of an object moving in circular path at constant speed. For our syllabus, we are mainly interested in objects moving in