Question

The earth’s radius is 6.37 × 10 6 m ; it rotates once every 24 hours. What is the earth’s angular speed? Viewed from a point above the north pole, is the angular velocity positive or negative? What is the speed of a point on the equator? 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?)

Answer 1

Answer:

a) the angular speed of the Earth's rotation is 7.272 × 10⁻⁵ rad/s.

b) Viewed from the North Pole, Earth's angular speed rotates in an anticlockwise direction. Therefore, the angular velocity is positive.

c) Earth's speed at a point on the equator is 463.23 m/s.

d)  the speed of a point on the earth’s surface halfway between the equator and the pole is 231.61 m/s.

Explanation:

a) The angular speed of the Earth's rotation is:

ω = 2π / T

where

T is the period

ω = 2π / (24 hr × (3600 s / 1 hr))

ω = 7.272 × 10⁻⁵ rad/s

b) Viewed from the North Pole, Earth's angular speed rotates in an anticlockwise direction. Therefore, the angular velocity is positive.

c) Earth's speed at a point on the equator is:

v = r × ω

v = (6.37 × 10⁶ m) × (7.272 × 10⁻⁵ rad/s)

v = 463.23 m/s

d) The radius of the circle in which the point moves is half of Earth's radius. Therefore,

r = 1/2(6.37 × 10⁶ m)

r = 3.19 × 10⁶ m

Therefore, the speed of a point on the earth’s surface halfway between the equator and the pole is:

v = r × ω

v = (3.19 × 10⁶ m) × (7.272 × 10⁻⁵ rad/s)

v = 231.61 m/s

Answer 2

A. The earth angular speed is $w=7.27*10^{-5} radian/s$

B. When viewed from the North Pole, the angular velocity is positive.

C. The speed of a point on the equator is 463 m/s

D. The speed of a point on the earth’s surface halfway between the        equator and the pole is 231.5 m/s.

Given that, radius of earth is, $r=6.37*10^{6} m$  and

          Time period $T=24 hours$

      $T=24hours=24*3600=86400seconds$

A. Earth angular speed,$w=\frac{2\pi}{T}=\frac{2*3.14}{86400}=7.27*10^{-5}radian/s$

B. When viewed from the North Pole, Earth's angular speed rotates in an anticlockwise direction. Therefore, the angular velocity is positive.

C.  The speed (v) of a point on the equator is,

                      $v=r*w\\\\v=6.37*10^{6} *7.27*10^{-5}=463 m/s$

D. The speed of a point on the earth’s surface halfway between the equator and the pole is,

               $v=\frac{r}{2}*w=\frac{463}{2}=231.5m/s$

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