During a very quick stop, a car decelerates at 7.20 m/s2. What is the angular acceleration (in rad/s2) of its 0.300 m radius tires, assuming they do not slip on the pavement? (Indicate the direction with the sign of your answer. Assume the tires initially rotated in the positive direction.)

To find the angular acceleration of the tires, we use the relationship between linear acceleration and angular acceleration:

\[
a = \alpha r
\]

Where:
- \(a\) is the linear acceleration of the car (\(-7.20 \, \text{m/s}^2\), negative due to deceleration),
- \(\alpha\) is the angular acceleration (what we are solving for),
- \(r\) is the radius of the tires (\(0.300 \, \text{m}\)).

### Solve for \(\alpha\):
\[
\alpha = \frac{a}{r}
\]

Substitute the values:
\[
\alpha = \frac{-7.20 \, \text{m/s}^2}{0.300 \, \text{m}} = -24.0 \, \text{rad/s}^2
\]

### Final Answer:
The angular acceleration of the tires is:
\[
\boxed{-24.0 \, \text{rad/s}^2}
\]

The negative sign indicates that the angular acceleration is in the opposite direction of the initial rotation (decelerating).

Would you like further details or have additional questions?

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### Related Questions:
1. What is the relationship between linear and angular velocity?
2. How does angular acceleration affect the rotational motion of an object?
3. If the car came to a stop in 2 seconds, what was the angular displacement of the tires?
4. How does the radius of the tire affect the angular acceleration?
5. What are the implications of tire slipping in this scenario?

### Tip:
Always check the signs carefully when working with accelerations and decelerations, as they determine the direction of motion or rotation.

During a very quick stop, a car decelerates at 7.20 m/s². What is the angular acceleration (in rad/s²) of its 0.300 m radius tires, assuming they do not slip on the pavement? (Indicate the direction with the sign of your answer. Assume the tires initially rotated in the positive direction.)

Learn how to calculate the angular acceleration of tires with a radius of 0.300 m when a car decelerates at 7.20 m/s². This problem explores kinematics, the relationship between linear and angular motion, and rotational deceleration. Suitable for high school students in Grades 11-12.

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