Final answer:
The angular speed of a point on Pluto's equator is 13752π radians per year and the linear speed is approximately 9626400π miles per year.
Step-by-step explanation:
To find the angular and linear speed of Pluto at its equator, we need to use the provided information about its rotation period and the radius of its equator.
Angular Speed
The angular speed (ω) of Pluto can be calculated using the formula ω = 2π / T, where T is the period of rotation. Since Pluto rotates once every 6 days, we first convert this period into years:
Period of Pluto's rotation in years: T = 6 days / 365 days/year = 1/365/6 years
Angular speed in radians per year: ω = 2π / (1/365/6) = 2π * 365 * 6 = 13752π radians/year
Linear Speed
The linear speed (v) of a point on the equator is given by the formula v = Rω, where R is the radius of the equator in miles.
Pluto's equatorial radius: R = 700 miles
Linear speed in miles per year: v = Rω = 700 miles * 13752π radians/year
v = 9626400π miles/year (approximately)