Uniform circular motion

Bodies in uniform circular motion

1. Francis Marlon Cabredo Mary Minette Ge ñ orga Mary Judith V erdejo

2. V Circular motion: Motion of a body along a circular path is known as circular motion. Uniform circular motion: Motion of a body long a circular path with the constant speed is called uniform circular motion . Circular motion

3. Uniform Circular Motion is the motion of an object in a circle with a constant or uniform speed UNIFORMCIRCULAR MOTION

4. SPEED V= 2 r T SPEED: In UCM, distance = the circumference of the circle T(period) is the time (or number of seconds) to make one revolution

5. PROBLEM 1: Tire Balancing Machine The wheel of a car has a radius of 0.29m and is being rotated at 0.072 sec/rev on a tire-balancing machine. Determine the speed (in m/s) at which the outer edge of the wheel is moving . Use 3.14 as the value for .

6. SOLUTION ANSWER 25 m/s

7. VELOCITY VELOCITY The velocity of an object in UCM has a constant magnitude and a constant change in direction The object does not have constant  velocity  since its direction changes at every point along the circle.   Also, The velocity is always tangent to the path of the object .

8. VELOCITY In UCM, the velocity is always tangent to the path of the object. The tangent specifies the direction of the motion . V A V D V B V C At a time t , the car is located at point A with a velocity of V A, this is tangent to the circle at point A. This means that… The direction of the velocity of the Car at point A is due west.

9. CENTRIPETAL ACCELERATION CENTRIPETAL ACCELERATION in UCM, an object has no constant velocity . Therefore, If there is a change in velocity, then that must mean that an object has acceleration. Centripetal   A cceleration . This acceleration has constant magnitude but changing direction and is directed radially inwards.

10. CENTRIPETAL ACCELERATION Symbol: a c Vector It is the rate of change of Tangential velocity Always perpendicular to the path of the motion. Points toward the center of the circle. V A V D V B V C A B C D

11. CENTRIPETAL ACCELERATION FORMULA:

12. PROBLEM 2 : Centripetal Acceleration The bobsled track at the 1994 Olympics in Norway , contained turns with radii of 33 m and 24 m, as the figure illustrates. Find the centripetal acceleration at each turn for a speed of 34 m/s, a speed that was achieved in the two-man event..

13. From a c =v 2 /r Radius=33m Radius=24m

14. 14 CENTRIPETAL FORCE

15. NEWTON’s SECOND LAW OF MOTION STATES THAT All accelerations are caused by a net force acting on an object.  In the case of UCM, the net force is a special force called the  centripetal force   .  

16. Centripetal is Latin for " center seeking ".  IT IS THE INWARD NET FORCE which keeps an OBJECT MOVING with a uniform velocity along A Circular path. This force is directed along the radius towards the center. CENTRIPETAL FORCE

17. APPLYING NEWTON’S SECOND LAW OF MOTION CENTRIPETAL FORCE Centripetal Force c a c =v 2 /r c c F=ma F c = mv 2 ___ r

18. N Newton N=kg m/s 2 UNIT USED:

19. PROBLEM 3A: Centripetal Force A 400-g rock attached to a 1.0-m string is whirled in a horizontal circle at a constant speed of 10.0m/s. Neglecting the effects of gravity, what is the centripetal force acting on the rock?

20. SOLUTION: Given: V=10.0 m/s R=1.0 m M=400g= 0.4 kg Find: Fc 20 F c = = (0.4 kg)(10 m/s) 2 ___________ 1.0 m mv 2 ___ r 40 N 40 kg m/s 2 = =

21. FORCES SUCH AS THE GRAVITATIONAL FORCE (w=mg), TENSION FORCE (tied to a string; pushing/ pulling), FRICTIONAL FORCE (Ex. a car turning) and Normal force (on a surface) can be the centripetal forces GRAVITATIONAL FORCE. For satellites in  orbit  around a  planet , the centripetal force is supplied by gravity.   TENSILE FORCE. For an object swinging around on the end of a rope in a horizontal plane, the centripetal force on the object is supplied by the tension of the rope. SOURCES OF CENTRIPETAL FORCE

22. THE centrifugal force ACTS AWAY FROM THE CENTER. The word itself means “fleeing from the center” . This force is a fictitious force . It doesn’t act on a body in motion, BUT only on non-inertial coordinate systems such as a rotating one. CENTRIFUGAL FORCE

23. PROBLEM 5: Which way will the object go? An object on a guideline is in uniform circular motion. The object is symbolized by a dot, and at point O it is release suddenly from its circular path . If the guideline is cut suddenly, will the object move along OA or OP ?

24. ANSWER: the object would move along the straight line between points O and A , not on the circular arc between points O and P .

25. SOLUTION: NEWTON’S LAW OF MOTION: “An object continues in a state of rest/ motion at a constant speed unless compelled to changes to its net force .” When the object was suddenly released from its path , there was no longer a net force (i.e. centripetal force) being applied to the object. 25 In the absence of a net force, the object will continue to move at a constant speed but, along a straight line in the direction it had at the time of release.

26. CENTRIFUGAL FORCE vs. INERTIA If you let go of the rope (or the rope breaks) the object will no longer be kept in that circular path and it will be free to fly off on a tangent.

27. 27 Uniform circular motion emphasizes that 1. The speed , or the magnitude of the velocity vector, is constant . 2. Direction of the vector is not constant . 3. Change in direction, means acceleration 4. “ Centripetal acceleration ” , points toward the center of the circle . 5. “ Centripetal Force ” is the net force that causes centripetal acceleration

28. Assignment: Solve the problems in the Practice Math in yourbook , page 19. (1/2 crosswise pad paper) Study for the Long Test on, July 18. Topics: Types of Forces, Friction, Laws of Motion, Uniform Circular Motion

29. AP PHYSICS Circular Motion Mrs. Coyle Practical ad Explorational Physics Padua et al You and The Natural world Physics Navaza , Valdes INTERNET YOUTUBE GOOGLE…….. SOURCES: Francis Marlon Cabredo Mary Minette Ge ñ orga Mary Judith V erdejo APPLICATIONS PROBLEMS