# Angular acceleration of a tire....not sure how to find radius

In summary, the problem involves a car tire rotating at 3.5 rev/s and then accelerating to 6.0 rev/s after traveling 200 m. The tire's angular acceleration is requested in rad/s2. The solution involves using the equation 2αΔΘ=ωf2-ωi2 and solving for the radius using the distance traveled and the tire's rotation. However, the given information does not include the radius, making it impossible to solve the problem accurately.

## Homework Statement

:[/B]
Your car tire is rotating at 3.5 rev/s when suddenly you press down hard on the accelerator. After traveling 200 m, the tire’s rotation has increased to 6.0 rev/s. What was the tire’s angular acceleration? Give your answer in rad/s2.

:[/B]
2αΔΘ=ωf2i2

## The Attempt at a Solution

:[/B]
We have 200m as a distance. With the absence of a tire's diameter, I tried (200 m)/(2πr rads) but again I don't know the radius. The book's solution manual uses ΔΘ=Δx/r and then simply states that the tire's radius is 32cm. I have no idea where this number came from.

leave delta phi as x / r. Also, don't translate rev / second into rad /s. Instead, translate rev into 2 pi r, and you'll find the r's cancel.

tony873004 said:
Instead, translate rev into 2 pi r, and you'll find the r's cancel.

I don't understand. Isn't the definition that rev=2π?

tony873004 said:
leave delta phi as x / r. Also, don't translate rev / second into rad /s. Instead, translate rev into 2 pi r, and you'll find the r's cancel.
There is only one variable which involves the dimension of distance. That makes it useless. There is simply not enough information.

## What is angular acceleration?

Angular acceleration is the rate of change of angular velocity of an object. It is a measure of how quickly an object is changing its rotational speed or direction.

## How is angular acceleration calculated?

Angular acceleration can be calculated by dividing the change in angular velocity by the change in time. This can be represented by the equation α = (ω2 - ω1) / (t2 - t1), where α is the angular acceleration, ω is the angular velocity, and t is the time.

## What factors affect the angular acceleration of a tire?

The angular acceleration of a tire can be affected by a few factors, including the force applied to the tire, the mass of the tire, and the radius of the tire. The shape and condition of the tire can also play a role.

## How does the radius of a tire affect its angular acceleration?

The radius of a tire can affect its angular acceleration because it determines the distance from the center of rotation to the points on the tire. A larger radius means a greater distance to travel, resulting in a higher angular acceleration. Similarly, a smaller radius will result in a lower angular acceleration.

## How can I find the radius of a tire if it is not provided?

If the radius of a tire is not provided, it can be calculated by dividing the circumference of the tire by 2π. This can be represented by the equation r = C / 2π, where r is the radius and C is the circumference. The circumference can be measured by wrapping a string around the tire and then measuring the length of the string.

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