PPT-Math 150 3.3 – The Unit Circle and Circular Functions

1 Recall Weve defined the sine function in two ways and   2 All the trig functions can also be defined in terms of the unit circle circle with radius 1 centered at the origin. A circle is defined to be the collection of all points ( x , y ) that are equidistant from afixed center point ( h , k r . Suppose a circle is centered at the origin (0, 0) and has a radius of lengt 2.4.1 Draw a vector diagram to illustrate that the acceleration of a particle moving with constant speed in a circle is directed towards the centre of the circle.. 2.4.2 Apply the expression for centripetal acceleration. . express angular displacement in radians. . understand and use the concept of angular velocity to solve problems. . recall and use . v = r. ω. to solve problems. . 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. . The Unit Circle. The Unit Circle. Has a radius of 1. Center at the origin. Defined by the equations:. a) . b) . The Unit Circle. The real number . t. corresponds to the distance around the unit circle.. Angular Measure, Angular Speed,. and Angular Velocity. Bellwork. . 1. A tube is been placed upon the 1 m-high table and shaped into a three-quarters circle. A golf ball is pushed into the tube at one end at high speed. The ball rolls through the tube and exits at the opposite end. Describe the path of the golf ball as it exits the tube.. This one’s going to be quick. Uniform Circular Motion. Uniform Circular Motion = an object following a circular path AT CONSTANT SPEED.. Why can we not say “at constant velocity”?. Definition: . Circular Motion Lab Results. Part 1: Radius’ effect on velocity. Mass, centripetal force kept constant. Part 2: Mass’ effect on velocity. Radius, centripetal force kept constant. Part 3: Force’s effect on velocity. Centripetal acceleration. Problem solving with . Newton’s 2nd Law . for . circular motion. Lecture 8: Circular motion. Effect of force components . Components of force parallel and perpendicular to velocity have different effects.. 5-1 Uniform Circular Motion. Uniform Circular Motion. : The motion of an object traveling at a constant (uniform) speed on a circular path. 5-1 Uniform Circular Motion. Since we are dealing with object moving in a circle, it is convenient to talk about the . , . Sitichai. . Srioon. , Chaiporn Jaikaeo. Department of Computer Engineering. Kasetsart University. Cliparts. are taken from . http://openclipart.org. . 01204111 Computers and Programming. Revised 2018-08-21. Can you change your velocity while not changing your speed?. v. F. Consider the above situation.. According to Newton . S. econd law, what must the object be doing?. It is accelerating so the velocity must be changing.. Unit Circle ( √3 , 1 ) 2 2 ( 1 , √3 ) 2 2 ( √2 , √2 ) 2 2 30˚ 45˚ 60˚ Use the Unit Circle to find cos 135 Reference angle: 45 Coordinate: x Lesson 6.1 – Functions that model a vibrating spring, an electrical current, and the horizontal range of a kicked soccer ball involve the two most important trigonometric functions. In the unit c (from 3.2 Trigonometry). KS3 Mastery PD Materials: Exemplified Key Ideas. Materials for use in the classroom or to support professional development discussions. Summer 2021. About this resource. These slides are designed to complement the .