- #1

crono_

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## Homework Statement

The differential gear of a car axle allows the wheel on the left side of a car to rotate at a different angular speed than the wheel on the right side. A car is driving at a constant speed around a circular track on level ground, completing each lap in 23.7 s. The distance between the tires on the left and right sides of the car is 1.50 m, and the radius of each wheel is 0.350 m. What is the difference between the angular speeds of the wheels on the left and right sides of the car?

t = 23.7 s

r = 0.350 m

d = 1.50 m

s = 2[tex]\pi[/tex]

[tex]\vartheta[/tex] = ?

[tex]\omega[/tex] = ?

## Homework Equations

[tex]\vartheta[/tex] = s / r

[tex]\omega[/tex] = [tex]\Delta[/tex][tex]\vartheta[/tex] / [tex]\Delta[/tex]t

## The Attempt at a Solution

I'm really drawing a blank on this...I think that I want to find out how many times the wheels spin during the 23.7 s it takes for one lap. Then that amount can be entered into the angular velocity equation to get their speed. As the question states that one wheel moves faster than the other, I'm thinking that the distance between the two wheels would help me figure out the difference...but I'm not sure how to work that distance in.

So, first I started out by trying to find the angular displacement [tex]\vartheta[/tex].

[tex]\vartheta[/tex] = s / r

[tex]\vartheta[/tex] = 2[tex]\pi[/tex][STRIKE]r [/STRIKE]/ [STRIKE]r[/STRIKE]

[tex]\vartheta[/tex] = 2[tex]\pi[/tex]

[tex]\vartheta[/tex] = 6.2831 rad

Then I attempted to find the angular velocity [tex]\omega[/tex].

[tex]\omega[/tex] = [tex]\Delta[/tex][tex]\vartheta[/tex] / [tex]\Delta[/tex]t

[tex]\omega[/tex] = 6.2831 rad / 23.7 s

[tex]\omega[/tex] = 0.26336 rad/s

After this though, I'm not sure where to go...assuming what I've done so far is correct. Any thoughts, suggestions, etc, would be appreciated.

Thank you!