Problem Set 6

# Problem Set 6 - Problem Set VI Assign October 9 2006 Due...

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Problem Set VI- Assign October 9, 2006 Due October 16. Fall 2006 Physics 200a Figures at the end R. Shankar Many problems ask for answers in terms of symbols and not numbers. You may need to invoke things like g in the answer even if I did not explicitly deﬁne them. 1. (i) What is the moment of inertia I CM of a propeller with three blades (treated as rods) of mass m , length L , at 120 0 relative to each other? (ii) If a torque τ acts on this how long will it take to reach an angular velocity ω ? (iii) How many revolutions will it have made before reaching this ω ? (iv) Get the numerical answers if L = 1 . 25 m , m = 12 kg , τ = 3000 N · m , ω = 2000 rads/s . 2. Consider I for a rectangle of sides a (along the y -axis) and b (along the x -axis ) about the two symmetry axes. (Rotate the rectangle about one of these axes and think of it as composed o of rods. ) Show that about the axis parallel to x , I = 1 12 Ma 2 . Going back to the very deﬁnition of I , show that if this rectangle is spun around an axis through its CM and perpendicular to its area the moment of inertia will be I = 1 12 M ( a 2 + b 2 ). 3. A 4

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## This note was uploaded on 07/13/2008 for the course PHYS 200 taught by Professor Ramamurtishankar during the Fall '08 term at Yale.

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Problem Set 6 - Problem Set VI Assign October 9 2006 Due...

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