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 20.2 s. The distance between the tires on the left and right sides of the car is 1.70 m, and the radius of each wheel is 0.400 m. What is the difference between the angular speeds of the wheels on the left and right sides of the car?

To find the difference between the angular speeds of the wheels on the left and right sides of the car, we can use the formula:

Δω = v / r

Where:
Δω is the difference in angular speeds
v is the linear speed of the car
r is the radius of each wheel

First, let's find the linear speed of the car using the formula:

v = 2πr / t

Where:
v is the linear speed of the car
r is the radius of each wheel
t is the time taken to complete each lap

Given:
r = 0.400 m
t = 20.2 s

Plugging in the values, we have:

v = 2π(0.400) / 20.2

Simplifying this, we get:

v = 0.125 m/s

Now, we can find the difference in angular speeds:

Δω = v / r

Plugging in the values:

Δω = 0.125 / 0.400

Simplifying this, we get:

Δω = 0.3125 rad/s

Therefore, the difference between the angular speeds of the wheels on the left and right sides of the car is 0.3125 rad/s.

To find the difference between the angular speeds of the wheels on the left and right sides of the car, we can use the formula:

Angular speed = Linear speed / Radius

We can start by finding the linear speed of the car. The linear speed can be determined by dividing the distance traveled by the time it takes to complete one lap. In this case, the distance is the circumference of the circular track.

Circumference = 2 * π * radius

Linear speed = Circumference / Time = (2 * π * 0.400 m) / 20.2 s

Linear speed = 0.06210197049076988 m/s

Now, we can determine the angular speed of each wheel by dividing the linear speed by the radius of the wheel.

Angular speed = Linear speed / Radius = 0.06210197049076988 m/s / 0.400 m

Angular speed = 0.1552549262279247 rad/s

Since the angular speed is the same for both wheels in this case, there is no difference in the angular speeds of the wheels on the left and right sides of the car.

the outer tire travels 2pi*1.7 = 10.68 m farther than the inside tire

Since the radius is .4 m, that's an extra 4.25 revolutions per lap

Since a lap takes 20.2 seconds, that's an extra

2pi*4.25 rad/20.2 s = 1.32 rad/s