Question

Saturn has a diameter of 74,900 miles. As the planet rotates on its axis, a point on its equator travels at 527,787 miles per day.

a. Find the angular speed of a point on its equator in radians per day.
b. Find the number of rotations the planet makes per day.

Answer 1

Answer:

a. ω = 14.1 radians per day

b. ω = 2.24 rotations per day

Explanation:

a.

The relationship between linear and angular velocity is given as:

v = rω

where,

v = linear speed of point = 527787 miles/day

r = radius of Saturn = diameter/2 = 74900 miles/2 = 37450 miles

ω = angular velocity of point = ?

Therefore,

527787 miles/day = (37450 miles)ω

ω = (527787 miles/day)/(37450 miles)

ω = 14.1 radians per day

b.

The number of rotations per day can be found by converting the units of angular acceleration:

ω = (14.1 radians per day)(1 rotation/2π radians)

ω = 2.24 rotations per day