A figure skater is spinning with an angular velocity of 12 rad/s.She then comes to a stop over a brief period of time. During this time, her angular displacement is 4.6 rad. Determine her average angular acceleration, in SI units, with 3 or more significant figures. Enter your answer without the unit.

To find the average angular acceleration, we can use the kinematic equation for rotational motion:

\[
\omega_f^2 = \omega_i^2 + 2 \alpha \theta
\]

where:
- \(\omega_f = 0 \, \text{rad/s}\) (final angular velocity, since she comes to a stop),
- \(\omega_i = 12 \, \text{rad/s}\) (initial angular velocity),
- \(\theta = 4.6 \, \text{rad}\) (angular displacement),
- \(\alpha\) is the average angular acceleration we want to find.

Rearrange the equation to solve for \(\alpha\):

\[
\alpha = \frac{\omega_f^2 - \omega_i^2}{2 \theta}
\]

Substitute the values:

\[
\alpha = \frac{0^2 - 12^2}{2 \times 4.6}
\]

\[
\alpha = \frac{-144}{9.2} = -15.6522
\]

Rounded to three significant figures, the average angular acceleration is:

\[
\alpha = -15.7
\]

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Would you like more details or have any questions about the steps?

Here are 5 related questions:
1. How would the answer change if the angular displacement was larger?
2. What would happen to the angular acceleration if she stopped in less displacement?
3. How is average angular acceleration different from instantaneous angular acceleration?
4. How can you calculate time if given only angular displacement and initial/final velocity?
5. How does linear acceleration relate to angular acceleration in circular motion?

**Tip:** When solving rotational problems, remember to keep units consistent, especially when dealing with radians and time

A figure skater is spinning with an angular velocity of 12 rad/s. She then comes to a stop over a brief period of time. During this time, her angular displacement is 4.6 rad. Determine her average angular acceleration, in SI units, with 3 or more significant figures. Enter your answer without the unit.

Learn to calculate the average angular acceleration of a figure skater who decelerates from 12 rad/s to a stop over an angular displacement of 4.6 rad. Explore key rotational motion concepts and apply kinematic equations for rotational dynamics. Suitable for students in Grades 10-12.

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