To find the mean angular speed of the minute hand of a clock, we need to determine the angular displacement and the time it takes to complete that displacement.
The angular displacement of the minute hand is equivalent to a full revolution or 360 degrees (2π radians), as it completes one full rotation in 60 minutes (1 hour).
The time it takes for the minute hand to complete this rotation is 60 minutes (1 hour) or 3600 seconds.
Therefore, the mean angular speed (ω) can be calculated as:
ω = angular displacement / time taken
ω = 2π radians / 3600 seconds
Simplifying the expression:
ω = π / 1800 radians per second
So, the mean angular speed of the minute hand of the clock is π / 1800 radians per second.