AP Physics - presentation L2.9 circular_motion.pptx

AP Physics

1. L2.9 Circular Motion

2. Circular Motion requires acceleration According to Newton’s Second Law, an object will move with constant speed in a straight line unless acted on by a force. A force is required to change an object’s speed, direction or both. An object moving in a circular path, even at constant speed, is constantly changing its direction and thus requires a force. What must be the direction and magnitude of this force?

3. Circular Motion You can make a ball tied to a string go in a circle by applying a tension which pulls the ball inward, toward the center of the circle, normal to its current velocity. Since the ball is acted on by a force, it must be accelerating toward the center of the circle. This acceleration is related to change in direction, not in tangential speed.

4. Centripetal Acceleration Even when tangential speed is constant, tangential velocity has changed due to change in direction. This indicates an acceleration. The centripetal acceleration is toward the axis of rotation.

5. Centripetal Force vs. Centrifugal Force To keep the object moving in a circular path, it must be forced to do so. This is the centripetal force . By the Law of Inertia, an object “wants” to move in a straight line, and so “feels” an apparent force pushing it outward. This is the apparent centrifugal force . The centripetal force drives the circular motion. The moving object “feels” a “centrifugal force” because of its non- inertial reference frame. Cause Felt

6. Centripetal Force

7. Loop- the- Loop In a loop-the-loop, the centripetal force is provided by the normal force.

8. Example A 1200- kg car rounds a curve of 45 m radius at 12 m/s. Find the centripetal force required to keep it on the circular path.

9. Example A 1200- kg car rounds a curve of 45 m radius at 12 m/s. Find the centripetal force required to keep it on the circular path.

10. Banked Curves Banking a curve can help keep cars from skidding. For every banked curve, there is one speed where the entire centripetal force can be supplied by the horizontal component of the normal force, and no friction is required. This occurs when: Ramp Speed 30 mph

11. Banking Planes also bank when turning so that lift provides the needed centripetal force.

12. Example While driving at 18 m/s, you encounter a dip in the road, which can be approximated as a 65 m radius arc. What is the normal force exerted by the car seat on a 81- kg passenger?

13. Example Similarly, the normal force exerted by a car seat is less when going over a small hill.

14. At the Top of the Loop- the- Loop

15. Spinning Bucket demo Q: Why doesn’t the water fall out? From the viewpoint of the water, this may be easier to understand as a “centrifugal force” holding it in. In the non- rotating frame, the explanation is conservation of momentum.

16. Centrifuge A centrifuge sorts out a mixture of liquids and solids by spinning. Conservation of linear momentum (“centrifugal force”) sends the more dense particles to the bottom of the tube. Centripetal acceleration

17. Example An puck, forced by a string, undergoes circular motion on a frictionless table. When the string breaks, what path will the object take? Answer: B, due to conservation of linear momentum.

18. Example What will be the child’s tilt for a given rotational speed?