1b) What is the angular speed with respect to the Earth\'s rotation axis of a pe

Question

1b)What is the angular speed with respect to the Earth's rotation axis of a person standing at a latitude of 52

What is the angular speed with respect to the Earth's rotation axis of a person standing at a latitude of 52 degree? A tree grows at an angle of 50 degree to the ground as shown in the figure below. If the tree is 29 m from its base to its top and has a mass of 450 kg, what is the magnitude of the torque on the tree due to the force of gravity? Take the base of the tree as the pivot point. (Assume the tree is a long clinder of uniform density. The answer reveals one reason trees need roots.) Consider the flagpole in the figure below. If the flagpole has a mass of 16 kg and length 10 m and the angle the cable makes with the pole is phi = 24degree, what are the magnitude and direction of the force exerted by the hinge (at point P) on the flagpole? Assume the mass of the pole is distributed uniformly. A solid cube of mass 35 kg and edge length 0.55 m rests on a horizontal floor as shown below. A person then pushes on the upper edge of the cube with a horizontal force of magnitude F. At what value of F will the cube start to tip? Assume the frictional force from the floor is large enough to prevent the cube from sliding.

Explanation / Answer

a point a latitude L has a radius of orbit around the polar axis equal to R cos L where R is the radius of the earth

so a point at 34 deg has a linear speed = 2 pi R cos L/86400s = 2*3.14*6370km cos 34/86400

linear speed = 0.384km/s = 384m/s

the earth rotates as a rigid body, so all points on the surface of the earth have an angular velocity of

2 pi rad/day = 2 pi rad/86400s = 7.3x10^-5 rad/s

w for a point on the equator is the same (as it is for all points on the surface of the earth), the linear speed is

linear speed = 2 pi R/86400s

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