Circular Motion. Unit 7

Transcription

1 Circular Motion Unit 7

2 Do Now You drive a car that follows a circular path with the radius r = 100 m. Find the distance travelled if you made one complete circle.

3 C 2 R 2(3.14)(100) 6.28(100) 628m

4 Uniform Circular Motion Suppose you are driving a car. If your car follows the path of a perfect circle with a constant radius, and speedometer reads the same speed, then you are experiencing uniform circular motion.

5 Rotation and Revolution Rotation - object turns around internal axis. Revolution object turns about an external axis.

6 Linear/Tangential Speed Linear Speed / Tangential Speed distance moved per unit of time. Linear speed dis tan ce time circumference time 2 r T T, period - time to move completely around the circle and return to the same place or to make one cycle around the circle. The direction of velocity at any instant is the direction of the tangent to the circle.

7 Linear/Tangential Speed Linear/Tangential Speed is directly proportional to the radius. The greater is the radius, the greater is the linear speed.

8 Check Question: If a meter stick supported at 0 cm mark swings like a pendulum from your fingers, how fast at any given moment the 100-cm mark moving compared to the 50-cm mark? Answer: The 100-cm mark is twice as far from the center of rotation as the 50-cm mark and so has twice the linear speed.

9 Frequency Frequency: f Frequency is the number of complete cycles per second f=1/t Units of Frequency: sec -1 Units of Frequency: Hz (Hertz) 1Hz = 1 cycle per second. For example, if the period is 0.5s, then the frequency is 2 cycles per second f 1 1 2s 1 Hz T 0.5s 2

10 Exercise If the period of orbit is 0.05 s, what is the frequency? 1 1 f 20Hz T 0.05s

11 Circular Motion and Change in Velocity An object moving in a circle experiences v acceleration. a t Even if moving around the perimeter of the circle with a constant speed, there is still a change in velocity and subsequently an acceleration. And in accord with Newton's second law of motion, an object which experiences an acceleration must also be experiencing a net force. F ma

12 Centripetal Force For an object moving in a circle, there must be an inward force acting upon it in order to cause its acceleration. The word centripetal (not to be confused with the F-word centrifugal) means center seeking. For object's moving in circular motion, there is a net force acting towards the center which causes the object to seek the center.

13 Acceleration According to the Second Law of Motion, net force and acceleration have the same direction. Inward centripetal force causes inward acceleration.

14 Centripetal Force

15 Centripetal Force

16 Do Now A rubber stopper is swung at the end of a string 0.95 m long with a period of 0.75 s. a) Compute the tangential speed of the stopper. b) Compute the frequency of the stopper c) If the string brakes, which path will the stopper follow?

17 a) b) 2 R m v T 0.75s f Hz T 0.75s 33 m s

18 Car Moving Around a Circle What force provides centripetal force required for circular motion? As a car makes a turn, the force of friction acting upon the turned wheels of the car provides centripetal force required for circular motion.

19 Bucket What force provides the centripetal force on a bucket? As a bucket of water is tied to a string and spun in a circle, the tension force acting upon the bucket provides the centripetal force required for circular motion.

20 What force provides centripetal force on the moon? As the moon orbits the Earth, the force of gravity acting upon the moon provides the centripetal force required for circular motion.

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22 Centripetal Force Required to Move an Object in a Circle Without a centripetal force, an object in motion continues along a straight-line path With a centripetal force, an object in motion will be accelerated and change its direction.

23 The Centripetal Force and Direction Change

24 Example You are riding in a car going around a curve. Sitting on your dashboard is a cassette tape. As you go around the curve, the tape moves to outside edge of the car. What force makes the cassette move?

25 Inertia vs. Centrifugal Force The tape on the slippery dashboard does not have enough friction to act as a centripetal force, so in the absence of a centripetal force the tape follows straight line motion. If the car you are riding in has the windows rolled down, then the tape will leave the car.

26 Centrifugal force is the name for the apparent force that pushes the object away from the center of a circle from the viewpoint of the object that undergoing circular motion. There is no force pushing the object away from the center of a circle, it is simply the object traveling in a straight line, tangent to the circle due to inertia.

27 Do Now A ladybug is sitting on a rotating platform relying on friction to avoid falling off. a) Draw a FBD for the ladybug. b)what is the direction of the force of friction? c) Is it static or kinetic? d) What will happen if the friction force too small to keep the bug in place?