Earth with mass M. The angular velocity magnitude of the Earth relative to the inertial frame,...
Earth with mass M. The angular velocity magnitude of the Earth relative to the inertial frame, Ω. Find any cross products in this problem.
This problem will have calculation in the non inertial frame S which rotates with the Earth about its axis. Earth is motionless in the S frame. The xyz coordinate system originates at the center of the Earth, the North Pole is on the positive z axis.
At t = 0, a ball of mass m is thrown with
Initial velocity = (-v0 cosθ0, 0, v0 sinθ0), initial position vector = (R sinθ0, 0, R cosθ0)
R = radius of Earth, θ0 = angle between 0 and pi/2
- Calculate the x, y, z components of the Coriolis Force on the ball when t = 0
- Calculate the x, y, z components of the Centrifugal Force on the ball when t = 0
- Calculate the x, y, z components of the Gravitational Force on the ball when t = 0
- When t is small the y value of the ball will be proportional to t2 where y = kt2. What is k?
Setting Ω to 0.
- Find the inertia tensor I of the point particle ball with respect to the xyz axes when t = 0.
- Calculate the angular momentum of the ball relative to the origin of the coordinate system when t = 0
Homework Answers
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Earth with mass M. The angular velocity magnitude of the Earth
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