Suppose that mercury rotates on its axis once every days. the equator lies on a circle with a radius of miles. (a) find the angular speed of a point on its equator in radians per year ( days). (b) find the linear speed of a point on the equator in miles per year. do not round any intermediate computations, and round your answer to the nearest whole number.

a)  w= 6 rad/day b) v = 2 10² m

Explanation:

Let's use angular kinematic relationships

a) The angular velocity is

    W = θ / t

     t = 1 day (24 h / 1 day) (3600s / 1 h) = 86400 s

    w = 2π / 86400

    w = 7.27 10⁻⁵ rad / s

Reduce to rad / day

   w = 7.27 rad / s (3600s / 1 h) (24 h / 1 day)

   w = 6.28 rad / day

   w= 6 rad/day

b) the linear velocity is

   v = w r

Mercury radius is

   r = 2.43 106 m

   v =  7.27 10⁻⁵ 2.43 10⁶

   v = 1.76661 10² m / s

   v = 2 10² m