DoDEA – Physics (SPC 501) - Standards

1. DoDEA – Physics (SPC 501) - Standards Pb.9 – Explain how torque () is affected by the magnitude (F), direction(Sin θ), and point of application of force (R).  = R*F(Sin θ) R = Torque Arm = distance between applied force and pivot point Pb.10 – Explain the relationships among speed, velocity, acceleration, and force in rotational systems. http://www.physicsclassroom.com/mmedia/circmot/circmotTOC.html

2. Circular Motion Circular motion (rotation) - When an object turns about an internal axis - motion of an object in a circlewith a constant or uniform speed (velocity???) - constant change in direction = acceleration • What is ?

3. Which “dot” (A-D) is traveling the fastest? • Angular Speed (ω)– the rate at which a body • rotates around an axis (rotations per minute = rpm) • Period - (cycle) – the time it takes to travel one revolution. • -- Object repeatedly finds itself back where it started. D C B A A B C D

4. SO, which “dot” (A-D) is traveling the fastest? • Radial Distance (r)– (radius) – distance from the axis (center) • Angular Displacement (θ)- the angle through which a point is rotated • C = 2 πr D C B A

5. Circular Motion is characterized by two kinds of speeds: - Tangential (v) (or linear) speed (circumference / t) - Angular speed (ω)(rotational or circular) (θ / t) A B C D Angular speed (ω) = “Clock hand speed”

6. Circular Motion—Tangential Speed Tangential speed(symbol v) - The distance traveled by a point on the rotating object divided by the time taken to travel that distance Points closer to the circumference (outer edge) have a higher tangential speed that points closer to the center.

7. Circular Motion – Rotational Speed Rotational (angular) speed - (symbol ) - is the number of rotations or revolutions per unit of time All parts of a rigid merry-go-round or clock hand turn about the axis of rotation in the same amount of time. – all parts have the same rotational speed Tangential speed  Radial Distance  Rotational Speed  = rxw

8. A ladybug sits halfway between the rotational axis and the outer edge of the turntable . When the turntable has a rotational speed of 20 RPM and the bug has a tangential speed of 2 cm/s, what will be the rotational and tangential speeds of her friend who sits at the outer edge? 1 cm/s 2 cm/s 4 cm/s 8 cm/s Rotational and Tangential Speed CHECK YOUR NEIGHBOR

9. A ladybug sits halfway between the rotational axis and the outer edge of the turntable . When the turntable has a rotational speed of 20 RPM and the bug has a tangential speed of 2 cm/s, what will be the rotational and tangential speeds of her friend who sits at the outer edge? 1 cm/s 2 cm/s 4 cm/s 8 cm/s Rotational and Tangential Speed CHECK YOUR ANSWER --Rotational speed (w) of both bugs is the same (w = 20 RPM) --So if the radial distance (r) doubles, tangential speed (v) will also double. --Tangential speed (v) is 2 cm/s  2 = 4 cm/s.  = rxw

10. Angular Displacement (θ)- the angle through which a point is rotated • Angular Speed (ω)– the rate at which a body rotates around an axis (rotations per minute = rpm) • Radial Distance (r)(radius) - distance from the central axis (center)

11. In circular motion, the direction of any “point” is constantly changing. Therefore, the velocity (speed with direction) is also constantly changing. v1 v2 A change in direction = A change in velocity = Accelerationa = Δv/t Acceleration only occurs when there is a net force applied to an object a = F/m In which direction must the FORCE be applied in order for an object to continue to travel in constant circular motion? Direction of Force = Direction of Acceleration

12. Centripetal Acceleration (Ac) – Acceleration directed toward the center of a circular path --Always points toward center of circle. --(Centripetal = center seeking) --Always changing direction! NOTE: Velocity is always in a straight line.

13. Any force directed toward a fixed center is called a centripetal force (Fc). The magnitude of the force required to maintain uniform circular motion. Acceleration only occurs when there is a net force applied to an object a = F/m Example: To whirl a tin can at the end of a string, you pull the string toward the center and exert a centripetal force to keep the can moving in a circle.

14. Centripetal Force (Fc) Depends upon: Mass (m) of object. Tangential speed (v) of the object. Radius (r) of the circle. CentripetalForce 2 m a s s t a n g e n t i a l s p e e d  = C e n t r i p e t a l f o r c e r a d i u s

15. Centripetal Force—Example When a car rounds a curve, the centripetal force prevents it from skidding off the road. If the road is wet, or if the car is going too fast, the centripetal force is insufficient to prevent skidding off the road.

16. Suppose you double the speed at which you round a bend in the curve, by what factor must the centripetal force change to prevent you from skidding? Double Four times Half One-quarter Centripetal Force CHECK YOUR NEIGHBOR

17. Suppose you double the speed (v) at which you round a bend in the curve, by what factor must the centripetal force (Fc) change to prevent you from skidding? Double Four times Half One-quarter Centripetal Force CHECK YOUR ANSWER 2 mass  tangential speed  Centripeta force radius Explanation: Because the term for “tangential speed” is squared, if you double the tangential speed, the centripetal force will be double squared, which is four times. The radius is constant. l WARNING: If you make a turn at double the speed, you are 4 timesmore likely to skid off of the road.

18. Suppose you take a sharper turn than before and halve the radius, by what factor will the centripetal force need to change to prevent skidding? Double Four times Half One-quarter Centripetal Force CHECK YOUR NEIGHBOR

19. Suppose you take a sharper turn than before and halve the radius; by what factor will the centripetal force need to change to prevent skidding? Double Four times Half One-quarter Centripetal Force CHECK YOUR ANSWER 2 mass  tangential speed  Centripeta l force radius Because the term for “radius” is in the denominator, if you halve the radius, the centripetal force will double. WARNING: The sharper your turn (smaller radius), the MORE likely you are to skid. The wider your turn (larger radius), the LESS likely you are to skid. What applies this centripetal force to the car???

20. Without a centripetal force, an object in motion continues along a straight-line path. An object will change direction ONLY if there is a NET force applied to the object. A CONSTANT force applied towards a central point results in a circular path Direction of Centripetal Force (Fc), Acceleration (Ac) and Velocity (v) Newton’s 1st Law

21. The cork will ONLY move while experiencing a net force (resulting in an acceleration). If I were to walk at a constant velocity, the cork would stay in the center.

22. Direction of Centripetal Force (Fc), Acceleration (Ac) and Velocity (v) Velocity (v) = straight line Force (Fc) = toward center Acceleration (ac) = toward center Acceleration occurs in the same direction as the applied force

23. 2 m a s s t a n g e n t i a l s p e e d  = C e n t r i p e t a l f o r c e r a d i u s A change in velocity is due to? (α)

24. 2 m a s s t a n g e n t i a l s p e e d  = C e n t r i p e t a l f o r c e r a d i u s What if the mass decreases?

25. 2 m a s s t a n g e n t i a l s p e e d  = C e n t r i p e t a l f o r c e r a d i u s What if the radius decreases?

26. A tube is been placed upon the table and shaped into a three-quarters circle. A golf ball is pushed into the tube at one end at high speed. The ball rolls through the tube and exits at the opposite end. Describe the path of the golf ball as it exits the tube. N

27. What provides the centripetal force? a) Tension b) Gravity c) Friction d) Normal Force Centripetal force is NOT a new “force”. It is simply a way of quantifying the magnitude of the force required to maintain a certain speed around a circular path of a certain radius.

28. Tension Can Yield a Centripetal Acceleration: If the person doubles the speed of the airplane, what happens to the tension in the cable? Doubling the speed, quadruples the force (i.e. tension) required to keep the plane in uniform circular motion.

29. Friction Can Yield a Centripetal Acceleration:

30. Centripetal Force: Question A car travels at a constant speed around two curves. Where is the car most likely to skid? Why? Smaller radius: larger force required to keep it in uniform circular motion.

31. Suppose two identical objects go around in horizontal circles of identical diameter but one object goes around the circle twice as fast as the other. The force required to keep the faster object on the circular path is _____the force required to keep the slower object on the path. 2 m a s s t a n g e n t i a l s p e e d  = C e n t r i p e t a l f o r c e r a d i u s The answer is E. As the velocity increases the centripetal force required to maintain the circle increases as the square of the speed. • the same as • one fourth of • half of • twice • four times

32. 2 m a s s t a n g e n t i a l s p e e d  = C e n t r i p e t a l f o r c e r a d i u s Suppose two identical objects go around in horizontal circles with the same speed. The diameter of one circle is half of the diameter of the other. The force required to keep the object on the smaller circular path is ___the force required to keep the object on the larger path. • the same as • one fourth of • half of • twice • four times The answer is D. The centripetal force needed to maintain the circular motion of an object is inversely proportional to the radius of the circle. Everybody knows that it is harder to navigate a sharp turn than a wide turn.

33. 2 m a s s t a n g e n t i a l s p e e d  = C e n t r i p e t a l f o r c e r a d i u s Suppose two identical objects go around in horizontal circles of identical diameter and speed but one object has twice the mass of the other. The force required to keep the more massive object on the circular path is • the same as • one fourth of • half of • twice • four times Answer: D.The mass is directly proportional to centripetal force.

34. Banked Curves Q: Why exit ramps in highways are banked? A: To increase the centripetal force for the higher exit speed.

35. How many forces are acting on the car (assuming no friction)? The Normal Force Can Yield a Centripetal Acceleration: Engineers have learned to “bank” curves so that cars can safely travel around the curve without relying on friction at all to supply the centripetal acceleration.

36. Banked Curves Why exit ramps in highways are banked? FN cosq = mg Fc = FN sinq = mv2/r The steeper the bank (q), the less friction is needed (more Force Normal is applied toward the center). This is why/how a race car track can allow cars to travel at such high speeds.

37. Gravity Can Yield a Centripetal Acceleration: Hubble Space Telescope orbits at an altitude of 598 km (height above Earth’s surface). What is its orbital speed?

38. The ride starts to spin faster and faster and you FEEL yourself being pushed back against the metal cage. Even when the ride starts to tilt skyward and you are looking DOWN at the ground, still you feel yourself almost “forced” back so that you do NOT fall to your death. EXPLAIN….

39. Centrifugal Force Although centripetal force is center directed, an occupant inside a rotating system seems to experience an outward force. This apparent outward force is called centrifugal force. Centrifugal means “center-fleeing” or “away from the center.” (The F-word) (The F-word)

40. Centrifugal Force – A Common Misconception It is a common misconception that a centrifugal force pulls outward on an object. Example: If the string breaks, the object doesn’t move radially outward. It continues along its tangent straight-line path—because no force acts on it. (Newton’s first law) (The F-word)

41. An inward net force is required to make a turn in a circle. This inward net force requirement is known as a centripetal force requirement. In the absence of any net force, an object in motion (such as the passenger) continues in motion in a straight line at constant speed. This is Newton's first law of motion. While the car begins to make the turn, the passenger and the seat begin to edge rightward. In a sense, the car is beginning to slide out from under the passenger. Once striking the driver, the passenger can now turn with the car and experience some circle-like motion. There is never any outward force exerted upon the passenger. The passenger is either moving straight ahead in the absence of a force or moving along a circular path in the presence of an inward-directed force. http://www.physicsclassroom.com/mmedia/circmot/rht.cfm

42. This path is an inward force - a centripetal force. That is spelled c-e-n-t-r-i-p-e-t-a-l, with a "p." The other word - centrifugal, with an "f" - will be considered our forbidden F-word. Simply don't use it and please don't believe in it. http://www.physicsclassroom.com/Class/circles/u6l1d2.gif

43. Rotating Reference Frames Centrifugal force in a rotating reference frame is a force in its own right – as real as any other force, e.g. gravity. • Example: • The bug at the bottom of the can experiences a pull toward the bottom of the can.

44. Why we use the f-word Centrifugal force in a rotating “reference frame” can be used to examine the simulation of gravity in space stations of the future. By spinning the space station, occupants would experience a centrifugal force (simulated gravity) similar to the bug in the can.

45. Simulated Gravity Have a radius of about 1 km (i.e. diameter of 2 km). Rotate at a speed of about1 revolution per minute. To simulate an acceleration due to gravity, g, which is 10 m/s2, a space station must:

46. Rotational Inertia An object rotating about an axis tends to remain rotating about the same axis at the same rotational speed unless interfered with by some external influence. The property of an object to resist changes in its rotational state of motion is called rotational inertia (symbol I).

47. Rotational Inertia Depends upon mass of object. distribution of mass around axis of rotation. The greater the distance between an object’s mass concentration and the axis, the greater the rotational inertia.

48. Rotational Inertia The greater the rotational inertia, the harder it is to change its rotational state. A tightrope walker carries a long pole that has a high rotational inertia, so it does not easily rotate. Keeps the tightrope walker stable.

49. Rotational Inertia Depends upon the axis around which it rotates Easier to rotate pencil around an axis passing through it. Harder to rotate it around vertical axis passing through center. Hardest to rotate it around vertical axis passing through the end.

50. Rotational Inertia The rotational inertia depends upon the shape of the object and its rotational axis.