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Chapter 8

Chapter 8. Rotational Motion. 1. CIRCULAR MOTION. Which parts on a merry-go-round move fastest? Which have greater rotational speeds? Examples of rotational motion: Earth rotates and revolves. 2. ROTATIONAL INERTIA. Law of inertia for rotating systems

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Chapter 8

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  1. Chapter 8 Rotational Motion

  2. 1. CIRCULAR MOTION • Which parts on a merry-go-round move fastest? • Which have greater rotational speeds? • Examples of rotational motion: Earth rotates and revolves

  3. 2. ROTATIONAL INERTIA • Law of inertia for rotating systems An object rotating about an axis tends to remain rotating at the same rate about the same axis unless interfered with by some external influence. • Examples: bullet, arrow, and earth • Demo – Football and Spinning Basketball • Demo - Whirly Tube (Zinger) • Demo – Whirly Shooter • Demo - Disc Gun • Demo - Rubber Bands

  4. Demo - Inertia Bars • Moment of inertia (rotational inertia) The sluggishness of an object to changes in its state of rotational motion • Distribution of mass is the key. • Example: Tightrope walker

  5. Demo - Ring and Disk on Incline • Demo – Metronome • Walking pendulums (bending knees)

  6. Demo – Falling Meter Sticks Lecture Table

  7. 3. TORQUE • Rotational analog of force • A torque changes the rotational state of motion. • Torque = force x lever arm length • It is a vector. • Units - N.m or lb.ft

  8. See-Saw F D = F D D D

  9. F D = F D 150 lb 50 lb 2 ft x

  10. l l l l Cheater Pipe Torque = Fl Torque = Fl F F F Torque = Fl Line of action of the force

  11. 4. CENTER OF MASS AND CENTER OF GRAVITY Center of mass - average position of mass Center of gravity - average position of weight . . Very large meteor Earth

  12. Path of center of mass of a rotating object will be a straight line if no external forces act on the object.

  13. Demo – Hammer Toss

  14. Locating the Center of Gravity • Demo – Meter Stick • Demo - Map of Texas • Demo - Balancing Eagle • Demo - Curious George • Demo – Picking Up Candy • Center can be outside of the object. • Examples: high jump and pole vaulting

  15. Stability • Demo - Tower of Pisa • Demo - Touching Toes • Demo - Standing on Toes • Demo - Object Rolling Uphill • Video – Dog Center of Mass • Demo - Boards Over the Edge 1/2 1/4 1/6 1/8

  16. Equilibrium - Unstable If an object is displaced slightly from equilibrium and released and the object moves to a new position, then the object was in a state of unstable equilibrium. Example: Ball on inverted bowl

  17. Equilibrium - Stable If an object is displaced slightly from equilibrium and released and the object returns to its old position, then the object was in a state of stable equilibrium. Example: Ball in bowl

  18. Equilibrium - Neutral If an object is displaced slightly from equilibrium and released and the object remains where it is, then it was in a state of neutral equilibrium. Example: Ball on horizontal surface

  19. 5. CENTRIPETAL FORCE • Centripetal force - center seeking force • Examples: tin can and string, sling, moon and earth, car on circular path, flying cat • Demo - Coin on Clothes Hanger • Demo - String, Ball, and Tube • Demo - Loop the Loop

  20. 6. CENTRIFUGAL FORCE • Centrifugal force - center fleeing force • Often confused with centripetal • Examples: sling and bug in can • Demo - Walk the Line • Centrifugal force is attributed to inertia.

  21. CENTRIFUGAL FORCE IN A ROTATING REFERENCE FRAME • A frame of reference can influence our view of nature. • For example: we observe a centrifugal force in a rotating frame of reference, yet it is a fictitious (pseudo) force. • Centrifugal force stands alone (there is no action-reaction pair) - it is a fictitious force.

  22. Another pseudo force - Coriolis

  23. 8. SIMULATED GRAVITY • To get a = g, the proper rotation rate and the proper radius must be determined. • Gravity gradients • Jogging in space

  24. 9. ANGULAR MOMENTUM For a point object the angular momentum is v J = mvr m Units - kg.m2/s or sl.ft2/s It is a vector. Here the vector is pointing toward you. r

  25. How do you change the angular momentum of an object? • An external torque is required. • Newton's first law for rotating systems: An object or system of objects will maintain its state of angular momentum unless acted upon by an unbalanced external torque.

  26. The larger J is, the larger the torque must be to change it. • Demo - Bicycle Wheel • Demo - Gyroscope

  27. 10. CONSERVATION OF ANGULAR MOMENTUM • If there are no external torques acting on a rotating system then angular momentum is conserved. • This means the final angular momentum is equal to the initial angular momentum.

  28. Examples: ice skater spin, diving, tides and moon • Demo - "Ice Skater“ • Movie – Ice Skater • Movie – SFA Cheerleaders • Demo - Bicycle Wheel and Rotating Platform • Movie - J in Sky Lab • Movie - More J in Sky Lab

  29. Chapter 8 Review Questions

  30. In walking, people normally bend their knees. Why? (a) it is easier to swing their legs because bending lowers the rotational inertia of their legs (b) it is easier to swing their legs because bending increases the rotational inertia of their legs

  31. Which is harder to stop? A rotating rod with its mass predominantly at the (a) middle of the rod (b) ends of the rod (c) neither of the above

  32. A ball is at rest on a horizontal table. It is in astate of equilibrium. (a) neutral (b) stable (c) unstable (d) both (a) and (b) (e) both (a) and (c)

  33. Which of the following forces is a pseudo force? (a) tension in a rope (b) force of gravity (c) centripetal (d) friction (e) centrifugal

  34. What is the angular momentum of a 6 kg mass traveling with a speed of 6 m/s in a circle of radius of 12 m? (a) 432 kg·m2/s (b) 12 kg·m2/s (c) 24 kg·m2/s (d) 144 kg·m2/s (e) 36 kg·m2/s

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