Answer :
Final answer:
The linear velocity of a point near the equator is calculated using Earth's angular velocity and its radius. It amounts to approximately 465.1 meters/second when considering Earth rotates every 24 hours and has a radius of 6.4 x 10⁶ meters at the equator.
Explanation:
The question asks for the linear velocity of a point near the equator of the Earth, given that Earth has a rotation period of 24 hours. To determine this, we must first calculate the Earth's angular velocity and secondly use it along with the radius of the Earth to calculate the linear velocity at the equator.
Answer Breakdown:
The period of rotation of Earth in seconds is 24 hours multiplied by 3600 seconds/hour, which equals 86,400 seconds.
The angular velocity (ω) of Earth is 2π radians per period, so ω = 2π radians / 86,400 seconds = 7.2722 x 10⁻⁵ radians/second.
With a radius of 6.4 × 10⁶ meters, the linear velocity (v) at Earth's surface can be calculated by the formula v = radius × angular velocity, which gives us v = 6.4 × 10⁶ m × 7.2722 x 10⁻⁵ rad/s. Therefore, the linear velocity is approximately 465.1 meters/second.
Note that the value provided for Earth's radius at the beginning of the question is in miles, but for the calculation, the metric system is used as it is the standard in physics calculations.
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Final answer:
The linear velocity of a point near the equator is approximately 1047.2 miles per hour.
Explanation:
To calculate the linear velocity of a point near the equator, we can use the formula v = rω, where v is the linear velocity, r is the radius of the Earth, and ω is the angular velocity.
The angular velocity can be calculated using the formula ω = 2π/T, where T is the period of rotation. In this case, the period of rotation is 24 hours.
Substituting the values into the formulas:
v = (4000 miles) * (2π/24 hours)
Simplifying the equation:
v = (4000 miles) * (π/12 hours)
Calculating the value:
v ≈ 1047.2 miles/hour
Therefore, the linear velocity of a point near the equator is approximately 1047.2 miles per hour.
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