A wheel makes 200 revolutions in 2 minutes. Find the measure of the angle it describes at the center in 24 second s. (In radian)
To find the measure of the angle the wheel describes at the center in radians, we need to know the angular velocity of the wheel.
The angular velocity is the rate at which the wheel rotates, measured in radians per second. It can be calculated using the formula:
angular velocity = (2 * π * number of revolutions) / (time in seconds)
In this case, the wheel makes 200 revolutions in 2 minutes. To convert this to seconds, we multiply by 60:
number of revolutions = 200
time in seconds = 2 minutes * 60 seconds/minute = 120 seconds
Plugging these values into the formula, we can calculate the angular velocity:
angular velocity = (2 * π * 200) / 120 = (2/3) * π radians/second
Now that we have the angular velocity, we can find the measure of the angle the wheel describes in 24 seconds. We can use the formula:
angle = angular velocity * time in seconds
In this case, the time is 24 seconds:
angle = ((2/3) * π) * 24 = (48/3) * π = 16π radians
Therefore, the measure of the angle the wheel describes at the center in 24 seconds is 16π radians.
200rev/2min * 4/10 min = 40rev
So, it has rotated through 80π radians.
However, it's not clear what "the angle" at the center is. At any rate, the wheel is exactly back to where it started after 40 complete revolutions.