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Exercise 1. Show that the force of gravity is central. (Note that this problem cannot be done without using the definition F = - Gmym2f of the force of gravity given on the previous page.) Let a particle of mass m move under the influence of a force F emminating from 0. Let: F(t) = the vector from Ō to the particle at time t T(t) = F" (t) = the velocity of the particle at time t a(t) = F"(t) = the acceleration of the particle at time t p(t) = mū(t) = the momentum of the particle at time t. %3D [(t) = F(t) x p(t) = the angular momentum. In handwritten work the notation r = |r| is common and convenient.

Exercise 1. Show that the force of gravity is central. (Note that this problem cannot be done without using the definition F = - Gmym2f of the force of gravity given on the previous page.) Let a particle of mass m move under the influence of a force F emminating from 0. Let: F(t) = the vector from Ō to the particle at time t T(t) = F" (t) = the velocity of the particle at time t a(t) = F"(t) = the acceleration of the particle at time t p(t) = mū(t) = the momentum of the particle at time t. %3D [(t) = F(t) x p(t) = the angular momentum. In handwritten work the notation r = |r| is common and convenient.

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Exercise 1. Show that the force of gravity is central. (Note that this problem cannot be done without using the definition F = - Gmym2f of the force of gravity given on the previous page.) Let a particle of mass m move under the influence of a force F emminating from ỡ. Let: F(t) = the vector from ở to the particle at time t T(t) = F"(t) = the velocity of the particle at time t a(t) = F"(t) = the acceleration of the particle at time t p(t) = mū(t) = the momentum of the particle at time t. I(t) = F(t) x p(t) = the angular momentum. In handwritten work the notation r = F is common and convenient.
Transcribed Image Text:Exercise 1. Show that the force of gravity is central. (Note that this problem cannot be done without using the definition F = - Gmym2f of the force of gravity given on the previous page.) Let a particle of mass m move under the influence of a force F emminating from ỡ. Let: F(t) = the vector from ở to the particle at time t T(t) = F"(t) = the velocity of the particle at time t a(t) = F"(t) = the acceleration of the particle at time t p(t) = mū(t) = the momentum of the particle at time t. I(t) = F(t) x p(t) = the angular momentum. In handwritten work the notation r = F is common and convenient.
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