A pendulum swings through an angle of 20 degrees each second. If the pendulum is 40 inches long, how far does its tip move each second?
to answer this question you need to know the formula for the circumference of a circle is: circumference = pi * 2r and a circle is 360 degrees.
so the length of the arc is what fraction of the whole circle?
and that fraction times the above circumference formula is your answer
To calculate how far the tip of the pendulum moves each second, we need to find the arc length of the swing.
Arc length can be calculated using the formula:
Arc length = (angle in radians) x (radius)
First, we convert the angle from degrees to radians. Since there are 360 degrees in a circle and 2π radians in a circle, we can use the formula:
angle in radians = (angle in degrees) x (π/180)
In this case, the pendulum swings through an angle of 20 degrees each second, so the angle in radians is:
angle in radians = 20 x (π/180)
Next, we multiply the angle in radians by the length of the pendulum (radius) to find the arc length:
arc length = (angle in radians) x (radius)
Given that the pendulum is 40 inches long, the arc length is:
arc length = (20 x (π/180)) x 40
To get the final answer, we can calculate this expression.
To find how far the tip of the pendulum moves each second, we need to calculate the arc length.
The arc length is given by the formula:
Arc length = (angle in degrees / 360) * (2 * pi * radius)
Given:
Angle in degrees = 20 degrees
Radius = 40 inches
Plugging in the values:
Arc length = (20 / 360) * (2 * pi * 40)
Simplifying:
Arc length = (1/18) * (2 * pi * 40)
Arc length = (1/9) * (pi * 40)
Arc length = (1/9) * (pi * 40)
Arc length = (40/9) * pi
Therefore, the tip of the pendulum moves approximately (40/9) * pi inches each second.