To find the angular displacement of a golf club that started from rest and reached a final angular velocity of 370°/s with a constant angular acceleration of 580°/s², we use the kinematic equation for rotational motion under constant angular acceleration:
[tex]\[ \theta = \frac{\omega^2 - \omega_0^2}{2 \alpha} \][/tex]
where:
- [tex]\(\theta\)[/tex] is the angular displacement,
- [tex]\(\omega\)[/tex] is the final angular velocity,
- [tex]\(\omega_0\)[/tex] is the initial angular velocity,
- [tex]\(\alpha\)[/tex] is the angular acceleration.
Given data:
- [tex]\(\omega_0 = 0\)[/tex] (the golf club started from rest),
- [tex]\(\omega = 370\)[/tex]°/s (final angular velocity),
- [tex]\(\alpha = 580\)[/tex]°/s² (constant angular acceleration).
First, we calculate the squares of the initial and final angular velocities:
- [tex]\(\omega_0^2 = (0)^2 = 0\)[/tex],
- [tex]\(\omega^2 = (370)^2 = 136900\)[/tex].
Next, we plug these values into the kinematic equation:
[tex]\[ \theta = \frac{136900 - 0}{2 \times 580} \][/tex]
Calculate the denominator:
[tex]\[ 2 \times 580 = 1160 \][/tex]
Now, divide the numerator by the denominator:
[tex]\[ \theta = \frac{136900}{1160} \][/tex]
[tex]\[ \theta = 118.01724137931035 \][/tex]
Therefore, the golf club rotated by approximately 118 degrees.
The correct answer is 118 degrees.
