Answer :
The constant angular acceleration of the wheel is approximately [tex]\( -5.17 \, \text{rad/s}^2 \).[/tex]
We can use the equations of rotational motion to solve this problem. The angular acceleration [tex]\( \alpha \)[/tex] can be calculated using the formula:
[tex]\[ \alpha = \frac{\omega_f - \omega_i}{t} \][/tex]
where [tex]\( \omega_f \)[/tex] is the final angular velocity, [tex]\( \omega_i \)[/tex] is the initial angular velocity, and t is the time interval.
Given that the wheel rotates 29.0 revolutions in 6.00 seconds, we first find the initial angular velocity [tex]\( \omega_i \)[/tex] in radians per second:
[tex]\[ \omega_i = \frac{2 \pi \times \text{number of revolutions}}{\text{time}} \][/tex]
[tex]\[ \omega_i = \frac{2 \pi \times 29.0}{6.00} \][/tex]
[tex]\[ \omega_i \approx 30.49 \, \text{rad/s} \][/tex]
Substituting the given values into the formula for angular acceleration:
[tex]\[ \alpha = \frac{97.0 \, \text{rad/s} - 30.49 \, \text{rad/s}}{6.00 \, \text{s}} \][/tex]
[tex]\[ \alpha = \frac{66.51 \, \text{rad/s}}{6.00 \, \text{s}} \][/tex]
[tex]\[ \alpha \approx -5.17 \, \text{rad/s}^2 \][/tex]
So, the constant angular acceleration of the wheel is approximately [tex]\( -5.17 \, \text{rad/s}^2 \)[/tex]. The negative sign indicates that the wheel is slowing down.
