0612345 Multiple-choice answer sheets: 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

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

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

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

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? m1 m2 T1 T2 T1 = T2 T1 < T2 T1 > T2 Physics 1D03

Atwood’s Machine R T2 T1 m2 m1 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

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

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

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

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

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