Circular kinematics a star in orbit around another star.

[lalalah]

i got part a, but i can't get part b!
1. A star has a mass of 2.96 x 10^30 kg and is moving in a circular orbit about the center of its galaxy. The radius of the orbit is 3.3 x 10^4 light-years (1 light-year = 9.5 x 10^15 m), and the angular speed of the star is 1.6 x 10-15 rad/s. (a) Determine the tangential speed of the star. (b) What is the magnitude of the net force that acts on the star to keep it moving around the center of the galaxy?

Homework Equations

F_c = m * a for centripetal force

a_c = V^2 /r

The Attempt at a Solution

I'm not sure if my idea for part b is right.
For part A, i got 501600 m/s.

I was wondering if the answer to part b would be attained by:
a_c = v^2 /r
a_c = 501600^2 / radius of orbit

using the radius of orbit given in the problem.

... and then, taking the calculated value for a_c and multiplying it by the given mass to give the F_centripetal.

is this correct reasoning? and sorry! my scientific calculator is located miles away, and my computer's calculator is a bit slow so i would rather punch in everything in the morning...
thanks!

 

[Hootenanny]

Yes, your method is completely valid.

 

[lalalah]

awesomeee. thanks for your help!

 

[lalalah]

ackkkk...

so when i punched out the answer, i got 2.38 x 10^21 N, and naturally, it doesn't fit in the answer type-in box! does anyone know if i did anything wrong? maybe my part a wasn't as correct as i thought it was...

i calculated part a using

V_t = w * r,

r = 33,000 Light years * (9.5 x 10^15 m)
r = 3.135 x 10^20


w = the given angular speed 1.6 x 10^-15

using the above equation, i got V_t = 501600.


is any of my work flawed whatsoever? eek!

 

[lalalah]

ahhhhhhh... so i found out that i should have punched in the answer as 2.4E21 instead of trying all the zeros! I'm an idiot. but thank you for all of the help! :)