Uniform (constant rotational rate) Circular Motion

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1 Uniform (constant rotational rate) Circular Motion

2 Uniform circular motion is the motion of an object in a circle with a constant speed and a constant radius.

3 Centrifugal Force (center fleeing) is an apparent outward force experienced by objects moving in a circle. It is fictitious because it would NEVER show up on a FBD. The sensation is not caused by a real force but rather the tendency of moving bodies to continue in a straight line unless there is a net force acting on them. CAUSED BY INERTIA (NOT A FORCE)! This goes back to Newton s 1st Law. F for FAKE, FICTIONAL, FAIL!!!!!

4 Centripetal Force (center seeking) (F c ) on the other hand is a real force. It is the unbalanced force that causes an object to turn. It always points/pulls to the center of the circle. It causes a centripetal acceleration(a c ) which also points to the center of the circle. Remember the direction of the acceleration is ALWAYS in the direction of the net force. It is a real force and does show up on FBD s. P = PASS!!!!

5 Newton s 1 st Law An object traveling at a constant speed in a straight line will continue in this motion unless acted upon by a net force Therefore an UNBALANCED or NET FORCE is required to cause an object to turn. This is the CENTRIPETAL FORCE (F c ) when looking at circular motion!

6 TURNING at a constant speed is CHANGING VELOCITY Velocity is the speed of an object as well as the direction of travel Speed is how fast an object is moving

7 A change in velocity requires an acceleration An object moving around a circle at a constant speed is changing velocity because it is turning

8 Draw the FBD and identify the centripetal force Hint: always identify the plane of the circle

9 Draw the FBD and identify the centripetal force Hint: always identify the plane of the circle

10 Draw the FBD and identify the centripetal force Hint: always identify the plane of the circle

11 Draw the FBD and identify the centripetal force Hint: always identify the plane of the circle

12 Draw the FBD and identify the centripetal force Hint: always identify the plane of the circle

13 What force (or forces) keeps the object in circular motion in the following picture? SKIP IT toy What direction is this force?

14 What force (or forces) keeps the object in circular motion in the following picture? Car turning on a level road What direction is this force?

15 Friction acts to hold the car along the curved road

17 Video Clip : Before we learn any Circular Motion Physics we need to let go of the concept of CENTRIFUGAL FORCE. IT DOES NOT EXIST!

18 Video Clip : Demonstration of centripetal acceleration with cork accelerometer

19 Video Clip : When the centripetal force goes away objects travel tangent to the circle. It moves in a straight line tangent to the edge of the circle.

20 Activity : Flying out tangent to the circle

21 Rotation vs. Revolution Does the earth revolve or rotate about it s axis? Does the earth revolve or rotate around the sun?

23 T = seconds cycle f = cycles second

24 Circular Motion Equations These are really an extension of Newton s 2 nd Law Σ F = ma! F c = ma c F c = centripetal force[n] the net center directed force that makes an object turn m = mass of the object moving in a circle [kg] é a c = centripetal acceleration m ù ë ê s 2 û ú the center directed acceleration What are some causes of centripetal force?

25 Circular Motion Equations (Continued) v = Circumference Time = 2pr T é v = Linear Speed (velocity) m ë ê s ù û ú r = radius[m] T = period or time to go around once [sec]

26 Circular Motion Equations (Continued) a c = v 2 r a c = centripetal acceleration é mù ë ê û ú s 2 r = radius[m] é v = linear speed m ë ê s ù û ú = 2pr T

27 Circular Motion Equations (Continued) When we substitute for centripetal acceleration we obtain the relationship below F c = mv 2 r F c = centripetal force[n] m = mass of the object moving in a circle [kg] é v = linear speed m ë ê s r = radius of the circle [m] ù û ú

28 Video Clip : Turntable Ride

29 The Gunslinger is modeled after the famed Flying Dutchmen rides of carnival midways. Guests ride in individual chairs suspended by tempered steel chains. The arms tilt to a 25 angle. As a safety engineer for the Six Flags of America Corporation, you are asked to determine the maximum allowable rotation rate for the Gunslinger if the breaking strength of the steel chains are 1000 N.

30 Other data: length of chain and swing: 4.5 m distance from center of rotation to chain attachment: 6.7 m 1. Draw a FBD of a rider and the swing 2nd Law Equations. 2. What is the source of the centripetal force acting on a rider and the swing? 3. Which will ride higher: an empty swing or one with someone in it? Explain. 4. Determine the maximum allowable rotation rate.

31 A ball held by a string is coasting around in a large horizontal circle. The string is then pulled in so the ball coasts in a smaller circle. When it is coasting in the smaller circle its speed is (Assume tension and mass stay constant) a) greater b) less c) Unchanged Explain.

32 Problem #1 If the radius of a circle is 1.5 m and it takes 1.3 seconds for a mass to swing around it (1 rev). a) What is the speed of the mass? b) Find the tension if the mass is 2 kg. s = 7.25 m/s F T = 70.1 N

33 Problem #2 A 1200 kg car traveling at 8 m/s is turning a corner with a 9 m radius. a) How large a force is needed to keep the car on the road? b) Find the coefficient of friction. F f = N μ =.726

34 Problem #3 A car travels around a circular flat track with a speed of 20 m/s. The coefficient of friction between the tires and the road is Calculate the minimum radius needed to keep the car on the track. r = m

35 Video Clip : Old clip of a Navy centrifuge used to test how many g s a pilot can take before blacking out

36 Video Clip : Old clip of the ride where the floor drops out and you stay stuck to the wall

37 Video Clip : The first looping coaster was located at Coney Island

38 Video Clip : How many g s can humans withstand?

39 Video Clip : Positive g s (not enough blood in brain) Negative g s (too much blood in brain)

40 Video Clip : Negative g s (too much blood in brain)

43 Bill the Cat, tied to a rope, is twirled around in a vertical circle. Draw the free-body diagram for Bill in the positions shown. Then sum the X and Y forces.

44 ΣF y = ma c F T + mg = mv²/r F T = mv²/r - mg F T = m ((v²/r) - g) a c W=mg F T ΣF y = ma c F T - mg = mv²/r F T = mv²/r + mg F T = m ((v²/r) + g) a c F T W=mg

45 Minimum velocity needed for an object to continue moving in a vertical circle. Any less velocity and the object will fall. At this point, F T = 0, so ΣF y = ma c F T + mg = mv²/r 0 + mg = mv²/r g = v c2 /r rg = v c 2 or, v c = rg

46 Suppose a car moves at a constant speed along a mountain road. At what places does it exert the greatest and least forces on the road? a) the top of the hill b) at the dip between two hills c) on a level stretch near the bottom of the hill Explain each case with a free body diagram and sum the forces.

48 Video Clip : Vertical loops

49 PHET Simulation Ladybug Revolution

50 Demonstration: Penny on hanger in vertical circle

B) v `2. C) `2v. D) 2v. E) 4v. A) 2p 25. B) p C) 2p. D) 4p. E) 4p 2 25

B) v `2. C) `2v. D) 2v. E) 4v. A) 2p 25. B) p C) 2p. D) 4p. E) 4p 2 25 1. 3. A ball attached to a string is whirled around a horizontal circle of radius r with a tangential velocity v. If the radius is changed to 2r and the magnitude of the centripetal force is doubled the