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Additional resources for A Guided Tour of Mathematical Physics

Example text

12) holds if and only if one of the vectors is a 16 Vector Operations scalar multiple of the other: u = Xv orv = Xu for some real number X; we have to write two conditions to allow either u or v, or both, to be the zero vector. 7. C Choose a Cartesian coordinate system (x,y,z) with the corresponding unit basis vectors (i, j , k). Let P, Q, be points with coordinates (1, —3,2) and (—2,4, - 1 ) , respectively. Define u = OP, v — OQ. (a) Compute QP = u — v, \\u\\, and \\v\\. Compute the angle between u and v.

I) Compute the angular momentum LQ of the point mass about O and the corresponding torque, (ii) Find the force F that is required to produce this motion, assuming the frame O is inertial. (Hi) Write F as a linear combination ofr and 6. (iv) How will the expressions simplify ifui(t) does not depend on time? 1, the Second Law of Newton implies the First Law. For further discussion of the logic of Newton's Laws see the book Foundations of Physics by H. Margenau and R. Lindsay, 1957. Regarding the First Law, they quote A.

12) between the accelerations in translated frames does not correctly describe acceleration of the point mass in the frame O in terms of the acceleration in the frame 0\.