Phys205A_Lecture32

# Physics for Scientists & Engineers with Modern Physics (4th Edition)

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Lecture 32 Midterm 4 Wednesday Nov 19 Topics: Rotation Center of mass Angular momentum Gravitation Chapter 13 Universal Gravitation Homework 10 Chapter 11 (angular momentum) Q 9,13 P 21,29 Chapter 13 Q 2,10 P 33

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Newton’s Law of Universal Gravitation z Every particle in the Universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the distance between them z G is the universal gravitational constant and equals 6.673 x 10 -11 N m 2 / kg 2 12 2 g mm FG r =
Law of Gravitation, cont z This is an example of an inverse square law z The magnitude of the force varies as the inverse square of the separation of the particles z The law can also be expressed in vector form z The negative sign indicates an attractive force 12 12 12 2 ˆ mm G r =− Fr r

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Notation z is the force exerted by particle 1 on particle 2 z The negative sign in the vector form of the equation indicates that particle 2 is attracted toward particle 1 z is the force exerted by particle 2 on particle 1 12 F r 21 F r
More About Forces z z The forces form a Newton’s Third Law action-reaction pair z Gravitation is a field force that always exists between two particles, regardless of the medium between them z The force decreases rapidly as distance increases z A consequence of the inverse square law 12 21 =− FF rr

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Gravitational Force Due to a Distribution of Mass z The gravitational force exerted by a finite- size, spherically symmetric mass distribution on a particle outside the distribution is the same as if the entire mass of the distribution were concentrated at the center z The force exerted by the Earth on a particle of mass m near the surface of the Earth is 2 E g E Mm FG R =
G vs. g z Always distinguish between G and g z G is the universal gravitational constant z It is the same everywhere z g is the acceleration due to gravity z g = 9.80 m/s 2 at the surface of the Earth z g will vary by location

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Finding g from G z The magnitude of the force acting on an object of mass m in freefall near the Earth’s surface is mg z This can be set equal to the force of universal gravitation acting on the object 2 2 E E E E Mm mg G R M gG R = =
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Phys205A_Lecture32 - Lecture 32 Midterm 4 Wednesday Nov 19...

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