A lighthouse rotates its light in a circular motion with a constant speed. If the beacon of light completes one rotation every 25 seconds,

what is the angular speed of the beacon in radians per minute?

Well, I hope you're ready for some math, because here we go!

To calculate the angular speed of the beacon in radians per minute, we first need to convert the time from seconds to minutes. There are 60 seconds in a minute, so we can divide 25 seconds by 60 to get the time in minutes.

25 seconds ÷ 60 seconds/minute = 0.4167 minutes

Now, we know that the beacon completes one rotation in 0.4167 minutes. Since one rotation is equal to 2π radians, we can divide 2π by 0.4167 to find the angular speed.

2π radians ÷ 0.4167 minutes = 15.079 radians/minute

So, the angular speed of the beacon is approximately 15.079 radians per minute. That's a lot of radians for a lighthouse! I hope it doesn't get dizzy.

To find the angular speed of the beacon in radians per minute, we first need to convert the rotation period from seconds to minutes.

Since there are 60 seconds in a minute, the rotation period in minutes is found by dividing the rotation period in seconds by 60:

Rotation period (minutes) = 25 seconds / 60 seconds/minute

Rotation period (minutes) = 0.4167 minutes

Now, to find the angular speed in radians per minute, we need to divide the angle of rotation (in radians) by the rotation period (in minutes).

Since the beacon completes one rotation every 25 seconds, the angle of rotation (in radians) is 2π radians (a full circle).

Angular speed (radians/minute) = 2π radians / 0.4167 minutes

Angular speed (radians/minute) ≈ 15.079 radians/minute

Therefore, the angular speed of the beacon in radians per minute is approximately 15.079 radians per minute.

To find the angular speed of the beacon in radians per minute, we need to first convert the time from seconds to minutes and then convert the angle from revolutions to radians.

1. Convert seconds to minutes: The given time period of one rotation is 25 seconds. To convert this to minutes, we divide by 60:

25 seconds ÷ 60 = 0.4167 minutes (rounded to four decimal places)

2. Convert revolutions to radians: Since the lighthouse completes one rotation in 25 seconds, we have one revolution. To convert revolutions to radians, we use the conversion factor (2π radians / 1 revolution):

1 revolution × 2π radians / 1 revolution = 2π radians

Now we have the time in minutes (0.4167 minutes) and the angle in radians (2π radians), so we can calculate the angular speed in radians per minute.

3. Divide the angle in radians by the time in minutes:

2π radians ÷ 0.4167 minutes = 15.084 radians per minute (rounded to three decimal places)

Therefore, the angular speed of the beacon in radians per minute is approximately 15.084.

2π radians every 25 seconds

x radians every 60 seconds

x/(2π) = 60/25
solve for x