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Answer :
The linear velocity of a point on the equator, given an angular speed of π/12 radian per hour and a radius of approximately 4000 miles, is calculated to be approximately 262 miles per hour.
To find the linear velocity at the equator, we can use the formula related to angular velocity (ω) and radius (r): v = r * ω. The angular speed given is π/12 radian per hour, and the equator's radius is approximately 4000 miles. So, substituting the values in the formula, we get:
v = 4000 miles * π/12 radian/hour = 1000π/12 miles/hour
To find the linear velocity in miles per hour, we calculate:
v ≈ 1000 * 3.14159 / 12 ≈ 1000 * 0.261799 ≈ 262 miles per hour.
Therefore, the linear velocity of a point on the equator is approximately 262 miles per hour.
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The linear velocity of the point on the equator is approximately 1047.197551 miles per hour.
The angular speed of a point on earth is pi/12 radian per hour. The equator lies on a circle of radius approximately 4000 miles. Find the linear velocity in miles per hour of a point on the equator.Since the linear velocity of a point on the equator is equal to the product of its angular velocity and its distance from the axis of rotation, it can be calculated using the given information.
That is,V=ω×rWhere,V is the linear velocity of the point on the equatorω is the angular velocity of the point on the equatorr is the radius of the earth (approximately 4000 miles)Substituting the values of ω and r, we have;V = ω×rV = π/12 rad/hr × 4000 miles
V = (4000π)/12 miles/hr
V = 1047.197551 miles/hr
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