Explanation:
a) The Earth makes 1 rotation in 24 hours. In seconds:
24 hr × (3600 s / hr) = 86400 s
b) 1 rotation is 2π radians. So the angular velocity is:
2π rad / 86400 s = 7.27×10⁻⁵ rad/s
c) The earth's linear velocity is the angular velocity times the radius:
40075 km × 7.27×10⁻⁵ rad/s = 2.91 km/s
(a)The period of rotation of Earth in seconds will be 86400 second.
(b) The angular velocity of Earth will be 7.27 ×10⁻⁵ sec.
(c)The linear velocity at Earth’s surface will be 2.91 km/sec.
The rate of change of angular displacement is defined as angular velocity.
It is stated as follows:
ω = θ t
Where,
θ is the angle of rotation,
t is the time
ω is the angular velocity
The period of rotation of Earth in seconds is found as;
As we know, the complete rotation of the earth took 24 hours.
The total rotational time is converted into the second;
1 hour = 3600 sec
24 hour=24×3600
T= 86400 second
The angular velocity of Earth is;
[tex]\rm \omega= \frac{2\pi}{T} \\\\\ \omega = \frac{2\times 3.14}{86400}\\\\ \omega = 7.27 \times 10^{-5} \ rad/sec[/tex]
The linear velocity at Earth’s surface is found as;
v=r ×ω
v=40075 ×7.27 ×10 ⁻⁵
v=2.91 km/sec
Hence, period of rotation, angular velocity of earth and linear velocity at Earth’s surface 86400 second,7.27 ×10⁻⁵ sec and 2.91 km/sec respectively.
To learn more about the angular velocity, refer to the link;
https://brainly.com/question/13649539
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