12. I The earth\'s radius is 6.37 X 10° m; it rotates once every 24 hours. a. Wh

Question

12. I The earth's radius is 6.37 X 10° m; it rotates once every 24 hours. a. What is the earth's angular speed? b. Viewed from a point above the north pole, is the angular velocity positive or negative? c. What is the speed of a point on the equator? d. What is the speed of a point on the earth's surface halfway between the equator and the pole? (Hint: What is the radius of the circle in which the point moves?) o throw a discus, the thrower holds it with a fully outstretched arm. Starting from rest, he begins to turn witha constant angular acceleration, releasing the discus after making one complete revolution. The diameter of the circle in which the discus moves is about 1.8 m. If the thrower takes 1.0 s to com-

Explanation / Answer

12)Given,

R = 6.37 x 10^6 m ; t = 24 hours = 86400 s

a)We know that

w = 2 pi f = 2 pi/T

w = 2 pi/T = 2 x 3.14/86400 = 7.27 x 10^-5 rad/s

Hence, w = 7.27 x 10^-5 rad/s

b)w will be positive as seen from equator.

c)We know that

v = r w

v = (6.37 x 10^6) (7.27 x 10^-5) = 463.1 m/s

Hence, v = 463.1 m/s

d)angle wrt equator at north pole will be:

theta = 30 deg

R' = R cos(theta) = 6.37 x 10^6 x cos30 = 5.52 x 10^6 m

v' = R' w = 5.52 x 10^6 x 7.27 x 10^-5 = 401.34 m/s

Hence, v' = 401.34 m/s

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