Centripetal Acceleration is a vector quantity because it

• Centripetal Acceleration is a vector quantity because it has both direction and magnitude. • Centripetal Acceleration is defined as an acceleration experienced by an object in uniform circular motion. • Centripetal acceleration is directed toward the center of the circle. • The acceleration depends on the changes of the velocity and since velocity is a vector, it can be changed in both magnitude or direction. So if a car is traveling in a circular path with a constant speed, the acceleration is due to a change in direction. This is called a centripetal acceleration. (Center-seeking)

• To calculate centripetal acceleration, you use the formula • • Ac =centripetal acceleration V=tangential speed/velocity R= Radius of a circle Ac is always perpendicular to the velocity

Ac = Centripetal Acceleration Ac = (v^2)/r v = 12 m/s r = 2 m 12^2 = 144/2 = 72 (D) 72 m/s^2

• While the object is in its uniform circular motion, there is a net force acting on it. • This force causes the centripetal acceleration. We call this force centripetal force. This force also goes toward the center of the circle. • The centripetal force is the net force on the circling object that acts to change the object’s direction. (There is no change in speed because there are no tangential forces acting on the object)

• • The centripetal force formula is Fc: Centripetal Force c M: mass Note: formula is obtained by newton’s second law. F=ma Ac: Centripetal Acc. • If the Centripetal force is removed, the object will move in a straight line (according to Newton’s first law) • Fc is perpendicular to the velocity

Fc = Centripetal Force Fc = m. Ac Ac = (v^2)/r m = 2 kg v = 6 m/s r = 10 m 6^2 = 36 36/10 = 3. 6 (2)(3. 6) = 7. 2 (A) 7. 2 m/s^2

(D) D Centripetal force is always directed towards center.

DEMO

Homework: • Amsco Pg 42; 192 • Amsco Pg 43; 203, 205