Using Figure 13.9, carefull sketch a free body diagram for the case of a simple pendulum hanging at latitude lambda, labeling all forces acting on the point mass, m . Set up the equations of motion for equilibrium, setting one coordinate in the direction of the centripetal accleration (toward P in the diagram), the other perpendicular to that. Show that the deflection angle ε , defined as the angle between the pendulum string and the radial direction toward the center of Earth, is given by the expression below. What is the deflection angle at latitude 45 degrees? Assume that Earth is a perfect sphere. tan ( λ + ε ) = g g − ω 2 R E tan λ , where ω is the angular velocity of Earth.
Using Figure 13.9, carefull sketch a free body diagram for the case of a simple pendulum hanging at latitude lambda, labeling all forces acting on the point mass, m . Set up the equations of motion for equilibrium, setting one coordinate in the direction of the centripetal accleration (toward P in the diagram), the other perpendicular to that. Show that the deflection angle ε , defined as the angle between the pendulum string and the radial direction toward the center of Earth, is given by the expression below. What is the deflection angle at latitude 45 degrees? Assume that Earth is a perfect sphere. tan ( λ + ε ) = g g − ω 2 R E tan λ , where ω is the angular velocity of Earth.
Using Figure 13.9, carefull sketch a free body diagram for the case of a simple pendulum hanging at latitude lambda, labeling all forces acting on the point mass,m. Set up the equations of motion for equilibrium, setting one coordinate in the direction of the centripetal accleration (toward P in the diagram), the other perpendicular to that. Show that the deflection angle
ε
, defined as the angle between the pendulum string and the radial direction toward the center of Earth, is given by the expression below. What is the deflection angle at latitude 45 degrees? Assume that Earth is a perfect sphere.
tan
(
λ
+
ε
)
=
g
g
−
ω
2
R
E
tan
λ
, where
ω
is the angular velocity of Earth.
Definition Definition Force on a body along the radial direction. Centripetal force is responsible for the circular motion of a body. The magnitude of centripetal force is given by F C = m v 2 r m = mass of the body in the circular motion v = tangential velocity of the body r = radius of the circular path
Using Figure 13.9, carefully sketch a free body diagram for the case of a simple pendulum hanging at latitude lambda, labeling all forces acting on the point mass, m. Set up the equations of motion for equilibrium, setting one coordinate in the direction of the centripetal acceleration (toward P in the diagram), the other perpendicular to that. Show that the deflection angle ε , defined as the angle between the pendulum string and the radial direction toward the center of Earth, is given by the expression below. What is the deflection angle at latitude 45 degrees? Assume that Earth is a perfect sphere. tan(λ + ε) = (g / (g − ω2 RE)) . tanλ , where ω is the angular velocity of Earth.
Consider a satellite in elliptical orbit around a planet of mass M, and suppose that physical units are so chosen that GM D 1 (where G is the gravitational constant). If the planet is located at the origin in the xy-plane, then Explain the equations of motion of the satellite?
Let T denote the period of revolution of the satellite. Kepler’s third law says that the square of T is proportional to the cube of the major semiaxis a of its elliptical orbit. In particular, if GM D 1, then?
In the Tsiolkovsky's equation, the parameter “delta v”, could I use “delta v”as “v” in the equation v=sqrt(GM/r) or are they different. For example if a satellite is in a geosynchronous orbit with a “delta v” of 2km/s, could I use the 2km/s to calculate the radius of orbit? Thanks
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