Rotational KINEMATICS (confusing)

[avenkat0]

Homework Statement

a) A 1.79 kg toy train accelerates constantly from 0.82 m/s to 3.43 m/s in 0.479 revolutions while traveling around a circular track of r 16.7 cm. Find:

- α, magnitude of the angular acceleration.

Homework Equations

The Attempt at a Solution

1. I first tried getting θ=(.479)(2pi)=3.009
2. Then I found both the ω_f and the ω_o by finding the frequencies... I did this by first finding the distence covered by the partial revolution then using the velocity. I did this for both the ω's...
3. Then i simply used the kinematic analog equation for rotational bodies and got α to be .00656 rad/sec² and this came out to be wrong

Is there a flaw in my reasoning
Thank You

 

[Doc Al]

Then I found both the ω_f and the ω_o by finding the frequencies... I did this by first finding the distence covered by the partial revolution then using the velocity. I did this for both the ω's...

I don't quite understand this step. Angular and tangential speeds are related by v = ωr.

 

[avenkat0]

Isn't w-2pi(f)

 

[Doc Al]

Isn't w-2pi(f)

Do you mean does ω = 2pi(f)? Sure, you could think of it that way, but I don't see the point. You are given the linear speeds and the radius, so the angular speeds can be found immediately. (But, done correctly, you should get the same answer either way. Does your method give you the same answer?)

 

[avenkat0]

Ooh so after I find the angular velocity I would just Use the equations to find alpha??

And can you also explain why the tangental and angular velocities are related by v=omega (r)... Will an object traveling at 5 m/s linearly be going at 2.5 rad/s because it's going around a circle with radius 2?

 

[Doc Al]

Ooh so after I find the angular velocity I would just Use the equations to find alpha??

Sure.

And can you also explain why the tangental and angular velocities are related by v=omega (r)... Will an object traveling at 5 m/s linearly be going at 2.5 rad/s because it's going around a circle with radius 2?

Yes.

Read this: Rotational Quantities