Name: Third Test Bonus, Page 5 of 6 Ape 12, 2018 4. The following quetions (part

Question

Name: Third Test Bonus, Page 5 of 6 Ape 12, 2018 4. The following quetions (parta) are to be coosidared lndependest questions to be r swered as stand alone problems. (1) (2 pointa) Calculate the angular velocity of a grandfather's clock socond and mitsute hand in rad/s and rpm. (II) (2 points) If the Earth's day were to get shorter by 86.4s, how much faster would a person in Earth's equator move around the Earth, as it rotates around its axis? (Radius of Earth 6371km.) (III) (2 points) If we consider Earth a sphere, how much rotational kinetic energy does it have from rotating around its own axis? (Mass of Earth -5.972 x 10kg.)

Explanation / Answer

4 (I) for second hand :

T = 60 s Or 1 m

w = 1 rpm

OR w = 2 pi / 60 = 0.105 rad/s

For minute hand:

T = 60 min OR 3600 s

w = 1 rev / 60 min = 16.7 x 10^-3 rpm ....Ans

w = 2 pi / 3600 s = 1.75 x 10^-3 rad/s .....Ans

(II) w = 2 pi / T and v = w r

vf - vi = (2 pi r ) (1/Tf - 1/Ti) = (2 pi r) (Ti - Tf) / T^2

delta(v) = (2 x pi x 6371 x 10^3)(86.4)/(24 x 3600)^2

= 0.463 m/s

(III) I = 2 M R^2 / 5

I = (2 x 5.972 x 10^24 ) (6371 x 10^3)^2 / 5

I = 9.696 x 10^37 kg m^2

w = 2 pi / T = 2 pi / (24 x 3600s) = 7.272 x 10^-5 rad/s  

KE = I w^2 /2 = 2.564 x 10^29 J

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