1. 0612345 Multiple-choice answer sheets:
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Multiple-choice answer sheets:
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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. 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

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. 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

6. 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

7. 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

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

9. 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

10. 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

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