Solving an Accelerating Car's Revolutions

[jjones1573]

Homework Statement

A car is coming to a top over a distance of 96m

Vi = 20m/s
r = 25cm

find the intial angular velocity, angular acceleration, total revolutions

Homework Equations

w = v / r
angular acceleration = change in w / t
d = (Vi + Vf / 2) t

The Attempt at a Solution

So for the initial angular velocity I did w = v / r
= 20m/s / 0.25m
= 80 rad/s

then I calculated the time based on displacement d = (Vi + Vf / 2) t
therefore t = d / (Vi + Vf / 2)
= 96 / 10
= 9.6s

So that I could find angular acceleration = change in w / t
= 80 / 9.6
= 8.3 rad/s

I THINK that's right so far

and for revolutions I did 80rad/s / 2phi
to get 12.7 rev/s

but then this is only the rate of rev/s at t=0 . This would decrease as the car deccelerates right? So how can I find the overal number of revolutions?

 

[gneill]

So how can I find the overal number of revolutions?

If you assume that the wheel doesn't slip on the road surface, then you should be able to count the number of wheel circumferences that go into the total distance.

 

[jjones1573]

Ah of course! that makes sense. What about in an instance where a ball is moving through the air, how could you measure the revolutions?

 

[gneill]

Ah of course! that makes sense. What about in an instance where a ball is moving through the air, how could you measure the revolutions?

Without non-slip contact with a surface there's no obvious way to fix a relationship between distance and revolutions -- the wheel could have any rotational velocity independent of linear speed.