Li Wei and his friend are conducting an experiment on pendulum motion.If their pendulum is 45cm and traverses an arc of 45cm, find, to the nearest degree, the rotation of the pendulum swing.
Question
Li Wei and his friend are conducting an experiment on pendulum motion.If their pendulum is 45cm and traverses an arc of 45cm, find, to the nearest degree, the rotation of the pendulum swing.
Solution
To solve this problem, we need to use the formula for the length of an arc of a circle, which is given by:
Arc length = radius * angle (in radians)
Here, the length of the pendulum is the radius of the circle, and the arc traversed by the pendulum is the arc length. We are asked to find the angle.
Given: Radius (r) = 45 cm Arc length (s) = 45 cm
We can rearrange the formula to solve for the angle:
Angle = Arc length / radius
Substituting the given values:
Angle = 45 cm / 45 cm = 1 radian
To convert radians to degrees, we use the conversion factor 180/pi:
Angle = 1 radian * (180/pi) degrees/radian ≈ 57.3 degrees
So, to the nearest degree, the rotation of the pendulum swing is approximately 57 degrees.
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