4. One day on the way to school, you had this thought: If a car tire with diameter centimeters is travelling at v kilometers per hour, then how would one represent the angular speed? Things that make you go hmmmm Determine the expression for the angular velocity in radians per second. 5. Consider the circle with centre B that passes through the point C. The circle cuts the line CA at D, and ADB is obluse. Part of the circle is shown below on the left. (a) Find ADB (b) Find the area of the shaded region. 6. The diagram above on the right shows a disc of radius 40 em with paris of it painted. The smaller circle(having the same center as the disc) has a radius of 10 cm. What area of the disc has not been painted? 7. The following diagram shows a circle with radius r and centre O. The points A, B and C are on the circle and A0C =#. The area of sector OABC is %" length of arc ABC is ETE Find the value of r and . 8. letp= sin40" and q = cos110. Find the following in rerms of p and q. (a) Write an expression for sin140" and cos70. (b) Find an expression for cos140. 10:58 93 Photo V Done netry.notebook 20H4614 ANGULAR VELOCITY: Radians are often used in applications involving rotational motion. This rotational motion, or circular motion, involves something called angular velocity. Definition: angular, Angular velocity is the rate at which the central angle is changing with respect-to time, dis tan ce travelled by central angle Angular Velocity time elapsed = angular distance_ AD G Time Time .Note: One revolution is equal to distance travelled by central angio feat radians. Example 4 Centralanglo = 30 x 21 = 6017 A car tire with a diameter of 64 cm, makes 30 revolutions in 5 seconds. (a) Determine the angular velocity, in radians per second A. V. = A.D. Time = 601 = 12TT sado/ second 5 (b) How far has the car travelled (n 2 minutes? This involves rotational motion and circles, which part of the circle should we *= 32 Cm consider? method) : a= ro revolutions O = angular distance in JI 20 seconds Methoda: 9= 127 X 120 circumference = /4 40 T Lads ( = 271) =271(32) a = (32 ) x 14 40 n E # revolutions 2min +