Through how many radians does the minute hand of a clock rotate in 50 min? In 7 h?
minute hand does one circle, 2 pi radians, in an hour
(50/60)*2 pi
7 * 2 pi
To calculate the rotation of the minute hand of a clock, we need to use the formula:
rotation = (time * 2π) / 60
Where "time" is the number of minutes or hours.
1. For 50 minutes:
rotation = (50 * 2π) / 60
rotation ≈ 5π/6 radians
Therefore, the minute hand rotates approximately 5π/6 radians in 50 minutes.
2. For 7 hours (420 minutes):
rotation = (420 * 2π) / 60
rotation ≈ 14π radians
Therefore, the minute hand rotates approximately 14π radians in 7 hours.
To calculate the angle in radians through which the minute hand of a clock rotates, we need to know that a complete rotation around a circle corresponds to 2π radians.
First, let's calculate the angle for 50 minutes. In one hour, the minute hand completes one full rotation (2π radians). So, in 60 minutes, the minute hand will also complete one full rotation. Since we have only 50 minutes, we can calculate the fraction of a full rotation that the minute hand completes:
Rotation for 50 minutes = (50 min / 60 min) * (2π radians)
Simplifying the expression, we get:
Rotation for 50 minutes = (5/6) * (2π) = (5π/3) radians
Therefore, the minute hand rotates through (5π/3) radians in 50 minutes.
Now, let's calculate the angle for 7 hours. In one hour, the minute hand completes one full rotation (2π radians). So, in 7 hours, the minute hand will complete 7 full rotations. We can calculate the angle in radians:
Rotation for 7 hours = 7 * (2π radians)
Simplifying the expression, we get:
Rotation for 7 hours = 14π radians
Therefore, the minute hand rotates through 14π radians in 7 hours.