What are the magnitudes of (a) the angular velocity, (b) the radial acceleration, and (c) the tangential acceleration of a spaceship taking a circular turn of radius 3610 km at a speed of 19600 km/hr?

Question

These were the answers I got, a and b were both wrong

a. 1809.695 (rad/s)

b. 11.82 (m/s^2)

c. 0 (m/s^2)

Answer 1

a)      The angular velocity is given by ω = V/R where V is the linear speed and R is the radius.

To get the units of radians per second, the linear speed must be expressed in km/s by dividing the speed by 3600 s/hr.

Ω = (19600 km/hr / 3600 s/hr) / 3610 km = 1.51 x 10^-3 radians/sec.

b)    The radial acceleration is given by a_R = ω^2 x R where R is expressed in meters.

a_R = (1.5 x 10^-3 rad/s)^2 x 3610 x 10^3 m = 8.12 m/s^2

Always check math.