# Simple conceptual rolling

1. Dec 6, 2006

### mbrmbrg

1. The problem statement, all variables and given/known data

A car travels at 75 km/h on a level road in the positive direction of an x axis. Each tire has a diameter of 60 cm.
Relative to a woman riding in the car, what are the following values?

(a) the velocity v at the center of each tire [0 m/s]
(b) the velocity v at the top of each tire [20.8 m/s]
(c) the velocity v at the bottom of each tire [-20.8 m/s]
(d) the magnitude a of the acceleration at the center of each tire [0 m/s^2]
(e) the magnitude a of the acceleration at the top of each tire [? m/s^2]
(f) the magnitude a of the acceleration at the bottom of each tire [? m/s^2]

Relative to a hitchhiker sitting next to the road, what are the following values?
(g) the velocity v at the center of each tire [20.83 m/s]
(h) the velocity v at the top of each tire [41.7 m/s]
(i) the velocity v at the bottom of each tire [0 m/s]
(j) the magnitude a of the acceleration at the center of each tire [0 m/s]
(k) the magnitude a of the acceleration at the top of each tire
(l) the magnitude a of the acceleration at the bottom of each tire

2. Relevant equations

1km/h=0.27778m/s
1m=100cm
$$a_c=\frac{v^2}{r}$$

3. The attempt at a solution

This is a relative motion problem: relative to the woman the wheels are rotating; relative to the hitchiker, the wheels are rolling.
I solved most of the problem, and gave my [correct] answers in brackets.

For the acceleration at the top and bottom of the wheel (parts e,f,k,&l):
First off, since both the woman and the hichiker are in inertial frames of reference, they will observe the same acceleration.
Secondly, since the woman sees the wheels as rotating, the acceleration at their rim is centripetal acceleration, and so
$$a=a_c=\frac{v^2}{r}=\frac{(20.83m/s)^2}{0.6m}=723m/s^2$$
As you probably assumed from the fact that I'm posting, this is INCORRECT (as are the answers 0, -723, and 721).

PS cool new format to force work to be shown... I think.

2. Dec 6, 2006

### Staff: Mentor

Nice work. I think the only error is using the diameter 0.6m as the radius in your angular acceleration calculation.

And thanks for the positive comment on the Homework Posting Template. Yeah, when it gets used, it's a huge help to us.

3. Dec 6, 2006

### mbrmbrg

thank you! and here I sit, insisting that I cannot understant torque, etc...
(derogitory term) stupid errors.