Find the angular speed in radians per sec. of the second hand on a clock.
How long does it take for the second hand to make one rotation?
And isn't one rotation 2pi radians?
Let me know what you got as an answer.
To find the angular speed in radians per second of the second hand on a clock, we need to first determine how long it takes for the second hand to make one full rotation.
One full rotation of the second hand on a clock takes 60 seconds, as there are 60 seconds in one minute. Therefore, it takes the second hand 60 seconds to complete one revolution.
Since one revolution is equivalent to going around a full circle, which is 360 degrees or 2π radians, we can say that the second hand completes one rotation in 2π radians.
Now, to find the angular speed in radians per second, we divide the angle traveled (2π radians) by the time taken (60 seconds):
Angular speed in radians per second = 2π radians / 60 seconds
Simplifying the expression, we get:
Angular speed = π/30 radians per second
Therefore, the angular speed of the second hand on a clock is π/30 radians per second.
Please note that the value of π is approximately 3.14159, thus the answer can be approximated as:
Angular speed ≈ 0.10467 radians per second.
So, the angular speed of the second hand on a clock is approximately 0.10467 radians per second.