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.
Well, let's see here. If the angular speed of a point on the planet is 3π/7 radians per hour, then we can find the linear velocity by multiplying this angular speed by the radius of the circle. In this case, the radius is approximately 9000 miles. So, all we have to do is multiply 3π/7 by 9000.
If you don't mind, I will do the math for you:
(3π/7) * 9000 ≈ 3857.14286 miles per hour.
So, the linear velocity of a point on the equator is approximately 3857.14286 miles per hour. But don't worry, you don't have to drive that fast just to keep up with the rotation of the Earth!
To find the linear velocity of a point on the equator, we need to multiply the angular speed by the radius of the circle.
Given:
Angular speed (ω) = 3π/7 rad/hr
Radius (r) = 9000 miles
Linear velocity (v) = ω * r
Substituting the values:
v = (3π/7) rad/hr * 9000 miles
Now, we need to convert radians per hour to miles per hour. We know that 2π radians is equivalent to the circumference of a circle.
Circumference (C) = 2π * r
Substituting the value of r:
C = 2π * 9000 miles
The linear velocity can be calculated as:
v = (3π/7) rad/hr * 9000 miles
Simplifying:
v = (3/7 * 2π) * (9000 miles) rad/hr
v = (6π/7) * (9000 miles)
Approximately:
v ≈ 38345.6 miles/hr
Therefore, the linear velocity of a point on the equator is approximately 38345.6 miles per hour.
To find the linear velocity of a point on the equator, we can use the formula:
Linear velocity = Angular speed x Radius.
Given that the angular speed of a point on the planet is 3π/7 radian per hour, and the equator lies on a circle of radius approximately 9000 miles, we can substitute these values into the formula to calculate the linear velocity.
Linear velocity = (3π/7) × 9000.
Now, let's simplify the expression:
Linear velocity = (3π × 9000) / 7.
Using the value of π as approximately 3.14159, we have:
Linear velocity ≈ (3 × 3.14159 × 9000) / 7.
Linear velocity ≈ 8466.3699 miles per hour.
Therefore, the linear velocity of a point on the equator is approximately 8466.3699 miles per hour.
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