Posted by **Alphonse** on Friday, October 26, 2012 at 2:03am.

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?

- Physics -
**Elena**, Friday, October 26, 2012 at 2:16am
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

- Physics -
**Alphonse**, Friday, October 26, 2012 at 2:30am
It gives me the wrong answer for some reason.

Thanks for the help though! I appreciate it.

- Physics -
**Elena**, Friday, October 26, 2012 at 2:39am
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

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