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Announcements

Announcements. Homework for tomorrow… (Ch. 12, Probs 9, 12, & 16) 11.54: α = 4.62 rad/s 2 Office hours… M 3-4 pm TWR 9-10 am F 1-2 pm Tutorial Learning Center – Houston Hall 113 MWR 8 am-6 pm T 8 am-7 pm F 8 am-5 pm.

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Announcements

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  1. Announcements • Homework for tomorrow… (Ch. 12, Probs 9, 12, & 16) 11.54: α= 4.62 rad/s2 • Office hours… M 3-4 pm TWR 9-10 am F 1-2 pm • Tutorial Learning Center – Houston Hall 113 MWR 8 am-6 pm T 8 am-7 pm F 8 am-5 pm

  2. Chapter 12 Complex Rotations (Combining Translations with Simple Rotations & The Vector Product)

  3. Section 12.2: Combining Translations with Simple Rotations Consider the motion of a yo-yo rolling down a string.. • the rolling motion is a combination of purely translational and purely rotational motion

  4. Quiz Question 1 A disk and a hoop with the same mass and radius are released together and roll down an inclined plane. The first object to reach the bottom is: • The disk • The hoop • Neither. They reach the bottom at the same time.

  5. Problem 11.63 A meter stick is held vertically with one end on the floor and is then allowed to fall. Find the speed of the other end when it hits the floor, assuming that the end on the floor does not slip. (Hint: Consider the stick to be a thin rod and use conservation of mechanical energy.)

  6. Example: Falling Spool At what rate does the body accelerate?

  7. Section 12.3:Rotational Variables as Vectors How can we work with rotational variables mathematically where the axes of rotation is changing direction? Consider a precessing top… …rotational variables can be expressed as 3D vectors

  8. Section 12.4: The Vector or Cross Product The vector or cross product is defined as… where the magnitude is: Note: • vectors a & b form a plane, vector c is  to the plane • Right hand rule gives the direction of vector c • c = area of the parallelogram formed by vectors a & b.

  9. The Cross Product, continued.. Notice: • A cross product (in terms of its components) is the determinant of a matrix

  10. Reading Exercise 12.1: Vectors c and d have magnitudes of 3 units and 4 units, respectively. What is the angle between the directions of vectors c & d if the magnitude of the vector product is • zero • 12 units • 6 units?

  11. Torque is defined as… where the magnitude of the torque is… Section 12.5: Torque as a Vector Product

  12. Touchstone Example 12.4: In Fig. 12.12a, three forces, each of magnitude 2.0 N, act on a particle. The particle is in the xz plane at point a given by position vector r, where r = 3.0 m and  = 30°. Force FAis antiparallel to the x-axis, force FBis antiparallel to the z-axis, and force FCis antiparallel to the y-axis. What is the torque, with respect to the origin O, due to each force?

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