1. C HAPTER 7 Circular motion

2. C IRCULAR MOTION Uniform circular motion can be described as the motion of an object in a circle at a constant speed. As an object moves in a circle, it is constantly changing its direction. At all instances, the object is moving tangent to the circle. Since the direction of the velocity vector is the same as the direction of the object's motion, the velocity vector is directed tangent to the circle as well. The animation at the right depicts this by means of a vector arrow.

3. E XAMPLE OF A CIRCULAR MOTION An example of circular motion is the ferris wheel

4. T ANGENTIAL SPEED The tangential speed ( v t ) of an object in circular motion is the object’s speed along an imaginary line drawn tangent to the circular path. Tangential speed depends on the distance from the object to the center of the circular path. When the tangential speed is constant, the motion is described as uniform circular motion.

5. C IRCULAR MOTION An object moving in a circle is accelerating. Accelerating objects are objects which are changing their velocity - either the speed (i.e., magnitude of the velocity vector) or the direction. An object undergoing uniform circular motion is moving with a constant speed. Nonetheless, it is accelerating due to its change in direction. The direction of the acceleration is inwards. The animation at the right depicts this by means of a vector arrow. The final motion characteristic for an object undergoing uniform circular motion is the net force. The net force acting upon such an object is directed towards the center of the circle. The net force is said to be an inward or centripetal force. Without such an inward force, an object would continue in a straight line, never deviating from its direction. Yet, with the inward net force directed perpendicular to the velocity vector, the object is always changing its direction and undergoing an inward acceleration.

6. C ENTRIPETAL ACCELERATION The acceleration of an object moving in a circular path and at constant speed is due to a change in direction. An acceleration of this nature is called a centripetal acceleration.

7. E XAMPLE #1 A test car moves at a constant speed around circular track. If the car is 48.2 m from the track’s center and has centripetal acceleration of 8.05 m/s^2, what is the car’s tangential speed?

8. E XAMPLE #2 Practice problem 1and 2 from page 226

9. S TUDENT GUIDED PRACTICE Do problems 3 and 4 page 226

10. C ENTRIPETAL FORCE Any motion in a curved path represents accelerated motion, and requires a force directed toward the center of curvature of the path. This force is called the centripetal force which means "center seeking" force. The force has the magnitudeforce Centripetal force= mass* (velocity square)/radius

11. E XAMPLE #3 A pilot is flying a small plane at 56.6 m/s in a circular path with radius of 188.5 m. The centripetal force needed to maintain the plane circular’s motion is 1.89 x10^4 N. What is the plane’s mass?

12. E XAMPLE #4 Do problem 2 page 228

13. S TUDENT GUIDED PRACTICE Do problems 1,3 and 4 in your book page 228

14. D ESCRIBING ROTATING MOTION To better understand the motion of a rotating system, consider a car traveling at high speed and approaching an exit ramp that curves to the left. As the driver makes the sharp left turn, the passenger slides to the right and hits the door. What causes the passenger to move toward the door?

15. CONTINUE As the car enters the ramp and travels along a curved path, the passenger, because of inertia, tends to move along the original straight path. If a sufficiently large centripetal force acts on the passenger, the person will move along the same curved path that the car does. The origin of the centripetal force is the force of friction between the passenger and the car seat. If this frictional force is not sufficient, the passenger slides across the seat as the car turns underneath

16. H OMEWORK Do worksheet problems 1-6 in the worksheet

17. CLOSURE Today we learned about circular motion, centripetal acceleration and force. Next we are going to learn about Newton’s law of universal gravitational