Analyzing Angular Motion in a Bicycle Wheel

[SkyChurch]

I'm stuck on this question: A rock stuck in the tread of a 59.0-{\rm cm}-diameter bicycle wheel has a tangential speed of 3.40 m/s. When the brakes are applied, the rock's tangential deceleration is 1.00 m/s^2.

a) What is the magnitudes of the rock's angular velocity at t = 1.70 s?
b) What is the magnitudes of the rock's angular acceleration at t = 1.70 s?
c) At what time is the magnitude of the rock's acceleration equal to g?

I've only really attempted part a so far and the equations I've used are: a(tangential)=r*a(angular) to find angular acc., v=r*w to find angular speed, and w final=w initial+a(angular)*t to find the angular speed at 1.7 s. I converted the radius, 29.5cm, to .295m and I'm getting 5.76 rad/s which is wrong. Where am I going wrong?

 

[Dr.D]

The wording of the problem, particularly parts b) and c), implies that the author thinks that the angular acceleration changes as time passes. In reality, this is almost certainly true, but there is nothing given in the problem statement, that I can see, to tell how this variation occurs.

I'd be interested in finding out what the intended solution for this problem is.

 

[SkyChurch]

It's an even numbered problem in the book so I have no idea what the answer is. I see what you're saying though.

 

[Dr.D]

The answers in the back of the book have been known to be wrong, but in this case I think the author of the problem intended something that neither of us is seeing. The question is, are we not seeing it because we are overlooking it, or are we not seeing it because he failed to tell us? I still do not see it. I suggest you ask your teacher at the first opportunity, and please post what you learn.

 

[SkyChurch]

this is an assignment on masteringphysics.com so that's how I know the answer's wrong. The website works in tandem with my physics book though, so if it was an odd numbered problem I'd at least be able to see what the answer is in the back of the book. The assignment's due at midnight tonight so if anyone else might have any idea please help.

 

[SkyChurch]

There was a glitch in the software for that problem because the whole class emailed the teacher telling him. So I was right for part a and part b you would just find the angular acc from the tangential acc. Part c you would take the square root of (radial acc)^2 + (tang acc)^2 to get the total acceleration and then go about solving for the time.