(a) Calculate the magnitude of the angular momentum of the earth in a circular orbit around the sun. Is it reasonable to model it as a particle? (b) Calculate the magnitude of the angular momentum of the earth due to its rotation around an axis through the north and south poles, modeling it as a uniform sphere. Consult Appendix E and the astronomical data in Appendix F.

Solution 38E The angular momentum can be calculated using the relation, L = mvr, where r is the perpendicular distance between the object and axis of rotation, m is the mass of the object and v is the linear velocity of the particle. When the earth orbits around the sun 7 Time period T = 365.3 days = 365.3 × 24 × 60 × 60 s = 3.15 × 10 s 2 Angular speed of the earth = T = 2×3.147rad/s 3.15×10 7 = 2 × 10 rad/s 11 Now, the orbital radius of earth is r0= 1.50 × 10 m 11 7 Linear speed of the earth v = r 0 = 1.50 × 10 m × 2 × 10 rad/s v = 3 × 10 m/s Now, mass of the earth m = 5.97 × 10 24kg (a) Now, substituting the values of m, v and r in th0 equation, L = mvr , we can calculate the angular momentum. L = 5.97 × 10 24kg × 3 × 10 m/s × 1.50 × 10 11m 40 2 L...