ASRJC Motion in a Circle Notes

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 6-1 Additional Notes: Topic 6: Motion in a Circle Content: • Kinematics of uniform circular motion • Centripetal acceleration • Centripetal force Learning Outcomes: Candidates 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 rv = to solve problems. Centripetal acceleration (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 2ra = and r va 2 = to solve problems. Centripetal force (f) recall and use centripetal force 2mrF = and r mvF 2 = to solve problems. Demonstrating Science Inquiry Skills In this chapter, we tackle key questions such as, “What causes an object to move in a circular path?”, “What is a centripetal force?” Relating Science and Society An example of an application of the concept of motion in a circle is the determination of the speed limit of vehicles negotiating a circular path. Other examples of motion in a circle include: • the rotation of the Earth about its axis, • the motion of the moon about the Earth (approximately circular), • the rotation of a compact disc about its axis, • the motion of a Ferris wheel, • the motion of the second, minute and hour hands of an analogue clock. Watch the human loop the loop on YouTube: https://youtu.be/ GkPudmBQBEY

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 6-2 Additional Notes: 6A Kinematics of Uniform Circular Motion 6A.1 Angular Displacement  Consider an object going round a circular path of radius r from point A to B. The angular displacement  is the angle the radius sweeps through in a specific direction from a reference line. s r=θ Note: • Since  is a ratio of a length to another length, it is dimensionless. •  is a vector quantity since it has direction (clockwise / anti-clockwise). Check Your Understanding 1 How many radians does 1° correspond to? A 0.035 rad B 0.0087 rad C 0.017 rad Recall that  rad = 180 Hence, =1 rad 180  r s A B O Definition of angular displacement: The angle through which an object turns, usually measured in radians (rad). Definition of a radian: 1 radian is the angle subtended by an arc of equal length to the radius. Legend: s: arc length r: radius of circle

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 6-3 Additional Notes: 22rv r r TT  = = = 6A.2 Angular Velocity  Definition: Angular velocity  is defined as the rate of change of angular displacement. d dt = θ Note: • Its unit is rad s−1. • It is a vector quantity. The direction pointing out of the page along the axis