Chapter 8.1, Problem 5PP

To determine

To Explain: The way angular velocity and number of revolutions would differ if larger diameter tires are used.

Explanation of Solution

Given:

Original tires are replaced by tires of larger diameter.

The speed of the car is same for both tires.

The distance covered by car is same for both the tires.

Formula used:

Angular velocity can be mathematically expressed as:

  $\omega =\frac{v}{r}$

Here, v is the linear velocity and r is the radius.

Number of revolutions, $n=\frac{\text{distance}}{2\pi r}$

Radius is half of diameter.

Calculations:

As the angular velocity and distance covered are inversely proportional to the radius (and hence, the diameter), with use of larger diameter tires, these quantities would decrease.

Conclusion:

Thus, the angular velocity and number of revolutions would decrease if larger diameter tires are used.