The angular speed of a point on a planet is 3pi/7 radian per hour. The equator lies on a circle of radius approximately 9000 miles. Find the linear velocity, in miles per hour, of a point on the equator.

Question

The angular speed of a point on a planet is 3pi/7 radian per hour. The equator lies on a circle of radius approximately 9000 miles. Find the linear​ velocity, in miles per​ hour, of a point on the equator.

Reiny · Answer

We don't know how many hours there are in 1 day of this fictitious planet

In "1 day" the point will have rotated 2πr or 18000π miles
Since one rotation is 2π radians and the change in the circumference is 3π/7 radians per hour, the number of hours in one day for this planet is
2π ÷ (3π/7) = 14/3 hours

speed along the circumference = 18000π ÷ (14/3) mph
= appr 12,118 mph

The angular speed of a point on a planet is 3pi/7 radian per hour. The equator lies on a circle of radius approximately 9000 miles. Find the linear​ velocity, in miles per​ hour, of a point on the equator.

The angular speed of a point on a planet is 3pi/7 radian per hour. The equator lies on a circle of radius approximately 9000 miles. Find the linear velocity, in miles per hour, of a point on the equator.