Question

You are riding a merry-go-round on the rim which is turning counterclockwise at a constant angular speed of 0.5 rad/s.  Your dog sees you at the 12 o'clock position when he is at the 3 o'clock position.  He starts running counterclockwise from rest with an angular acceleration of 0.31 rad/s2.  The merry-go-round has a radius of 3.36 m.
 
a) When does your dog first catch up to you?

b) How fast is your dog running (in m/s) at the instant you computed in part a?

Answer 1

Man: φ=ω•t
Dog: φ=ε•t²/2
ω•t= ε•t²/2
t=2 ω/ ε=2•0.5/0.31 =3.23 s
ω(dog) = ε•t=0.31•3.23= 1 rad/s

Answer 2

It gives me the wrong answer for some reason.

Thanks for the help though! I appreciate it.

Answer 3

Man: φ =ω•t
Dog: φ –π/2=ε•t²/2
ω•t= ε•t²/2 +π/2
ε•t² -2 ω•t+π=0
t={2±sqrt(4-2•3.14•0.31}/2•0.31
t1=3.74 s, t2 = 1.48 s
ω(dog) = ε•t=0.31•1.48= 0.459 rad/s