the end of a 40 inches pendulum describe an arc of 5 inches through what angle does the pendulum swing?
1/8 radian = 7.16 degrees
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To find the angle through which the pendulum swings, you can use the arc length formula:
Arc Length = Radius * Angle
In this case, the radius is the length of the pendulum, which is 40 inches, and the arc length is 5 inches. Plugging these values into the formula, we have:
5 inches = 40 inches * Angle
To solve for the angle, we can rearrange the equation:
Angle = 5 inches / 40 inches
Calculating this:
Angle = 0.125
Therefore, the pendulum swings through an angle of approximately 0.125 radians.
To determine the angle through which the pendulum swings, we can use the concept of an arc length formula. Here's how you can calculate it:
1. Recall that the arc length formula, given the radius of a circle (in this case, the length of the pendulum) and the angle (in radians), is given by:
arc length = radius * angle
2. In this case, the pendulum's length is 40 inches, and the arc length is given as 5 inches. Substituting these values into the formula, we have:
5 inches = 40 inches * angle
3. To find the angle, divide both sides of the equation by 40 inches:
angle = 5 inches / 40 inches
4. Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 5:
angle = 1/8
5. Therefore, the pendulum swings through an angle of 1/8 radians.
Note that the angle is given in radians, not degrees. To convert it to degrees, you can use the conversion factor: 1 radian = 180 degrees / π.