1.) The Earth can be approximated as a sphere of mass 6.0 x 10^24 kg and radius

Question

1.) The Earth can be approximated as a sphere of mass 6.0 x 10^24 kg and radius of 6.4 x 10^6 m. What is the rotational inertia of the Earth?
a.) 2.4 x 10^38 kg m2 b.) 1.2 x 10^38 kg m2 c.) 4.9 x 10^37 kg m2 d.) 9.8 x 10^37 kg m2

2.) What is the linear velocity of a point on the Earth's Equator as the Earth spins about its axis?
a.) 1047 m/s b.) 465 m/s c.) 370 m/s d.) 55 mph e.) 0 m/s

3.) What is the rotational kinetic energy of the Earth as it rotates about its axis?
a.) 2.6 x 10^29 J b.) 3.7 x 10^30 J c.) 7.1 x 10^33 J d.) 9.6 x 10^47 J e.) 7.27 x 10^-5 J

4.) What is the angular momentum of the Earth as it rotates about its axis?
a.) 2.6 x 10^29 kg m2/s b.) 3.7 x 10^30 kg m2/s c.) 7.1 x 10^33 kg m2/s d.) 9.6 x 10^47 kg m2/s e.) 7.27 x 10^-5 kg m2/s

5.) The Earth rotates counterclockwise when viewed looking down into the North Geographic Pole. The angular momentum vector desccribing the Earth's rotation points:
a.) up through the North Pole along the Earth's axis b.) counterclockwise around the Earth's Equator c.) down through the South Pole along the Earth's axis

Explanation / Answer

1)

I = (2/5)*m*R^2

I = (2/5)*6*10^24*(6.4*10^6)^2

I = 9.8*10^37 kg m^2

option (d)

(2)

v = R*w = R*2pi/T

v = 6.4*10^6*2*pi/(24*60*60)

v = 465 m/s

option (b)

++++++++++++

(3)

KEr = 0.5*I*w^2

w = v/R

KEr= 0.5*(2/5)*m*R^2*v^2/R^2

KEr = (1/5)*m*v^2

KEr = (1/5)*(1/5)*6*10^24*465^2^2

KEr = 2.6810^29 J

option (a)

++++++++++

4)

L = I*w = (2/5)*m*R^2*v/R

L = (2/5)*m*R*v

L = (2/5)*6*10^24*6.4*10^6*465

L = 7.1*10^33kg m^2/s

++++++++++

(5)

a.) up through the North Pole along the Earth's axis

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