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A golf club started from rest and reached a final angular velocity of 370°/s with a const; at angular acceleration of 580%/s². How many degrees did the club rotate?
210
118
156
213


Sagot :

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.