Question

Pluto has a diameter of 1400 miles. As the planet rotates on its axis, a point on its equator travels at 267,558 miles per year Find the angular speed of a point on its equator in radians per year.

Answer 1

To find the angular speed of a point on Pluto's equator in radians per year, we can use the formula: angular speed = linear speed / radius. The linear speed can be calculated by multiplying the distance traveled per year by 2π, and then divide the linear speed by the radius of Pluto to find the angular speed.

Step-by-step explanation:

To find the angular speed of a point on Pluto's equator in radians per year, we can use the formula:

angular speed = linear speed / radius

The linear speed can be calculated by multiplying the distance traveled per year by 2π, since one revolution around the planet's equator is equal to 2π radians. So the linear speed is 267,558 miles/year * 2π = 1,682,489 miles/year.

Now, we can divide the linear speed by the radius of Pluto to find the angular speed. The radius of Pluto is half of its diameter, so the radius is 1400 miles/2 = 700 miles. Dividing the linear speed by the radius gives us an angular speed of 1,682,489 miles/year / 700 miles = 2403 radians/year.