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0612345. Version number. Multiple-choice answer sheets: HB pencil only; ink will not work Fill circle completely No extra marks in answer area Erase well to change an answer. J. P. Student. Rotational Dynamics. Examples involving t = I a Parallel-axis theorem.

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  1. 0612345 Version number Multiple-choice answer sheets: HB pencil only; ink will not work Fill circle completely No extra marks in answer area Erase well to change an answer J. P. Student Physics 1D03

  2. Rotational Dynamics Examples involving t = I a Parallel-axis theorem Text sections 10.5, 10.7 Physics 1D03

  3. I=MR2 I = ½ MR2 L L I = 1/3 ML2 I = 1/12 ML2 Moments of inertia for some familiar objects: (see Table 10.2 in the text for more): You do not have to know how to derive any of these ! Physics 1D03

  4. QUIZ: If m1 > m2, the magnitudes of the accelerations of the masses obey the relation: • a1 > a2 • a1 = a2 • a1 < a2 • d) not enough info R2 R1 m1 m2 Physics 1D03

  5. T2 T1 m2 m1 Quiz: Atwood’s Machine, again Two masses, m1 > m2, are attached to the end of a light string which passes over a pulley. The pulley rotates (ie: there is friction between the pulley and string) on a frictionless horizontal axis and has mass M. How do the tensions in two sections of the string compare? • T1 = T2 • T1 < T2 • T1 > T2 Physics 1D03

  6. T2 T1 m2 m1 Atwood’s Machine • m1 = 3 kg, m2 = 2 kg, R = 10 cm. • Find the accelerations, tensions if • the string is massless • the pulley has moment of inertia I = 0.04 kg m2 . R a =1.09 m/s2, T1 = 26.1 N, T2 = 21.8 N Physics 1D03

  7. Parallel Axis Theorem I ICM I = ICM + MD2 D ICM : for an axis through the centre of mass I : for another axis, parallel to the first Physics 1D03

  8. Example: Uniform thin rod L/2 ICM = (1/12) ML2 I = (1/3) ML2 Since: I = ICM + MD2 Physics 1D03

  9. P CM Example: Uniform thin hoop (mass M, radius R); axis perpendicular to hoop P ICM = MR2 (why?) CM IP = ICM + MD2 (here “D” = R) = 2 MR2 Physics 1D03

  10. Example – 2 ways to solve a problemThe metre stick is pivoted at the 25-cm mark. What is its angular acceleration when it is released? Physics 1D03

  11. Summary Newton’s 2nd law for rotation about a fixed axis: Parallel-axis Theorem: I=ICM+MD2 Practice: Look over Examples in Chapter 10 Physics 1D03

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