Answer:
a) the angular speed of the Earth's rotation is <em>7.272 × 10⁻⁵ rad/s.</em>
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b) Viewed from the North Pole, Earth's angular speed rotates in an anticlockwise direction. Therefore, the <em>angular velocity is positive.</em>
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c) Earth's speed at a point on the equator is <em>463.23 m/s.</em>
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d) the speed of a point on the earth’s surface halfway between the equator and the pole is <em>231.61 m/s.</em>
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))
<em>ω = 7.272 × 10⁻⁵ rad/s</em>
b) Viewed from the North Pole, Earth's angular speed rotates in an anticlockwise direction. Therefore, the <em>angular velocity is positive.</em>
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)
<em>v = 463.23 m/s</em>
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)
<em>v = 231.61 m/s</em>
