A gymnast on a high bar swings through two revolutions in a time of 1.90s. Find the angular velocity of the gymnast
2 rev * 2 pi radians/rev = 4 pi radians
so
omega = 4 pi radians / 1.9 seconds
To find the angular velocity of the gymnast, we can use the formula:
Angular velocity (ω) = (2π * Number of revolutions) / Time
Given that the gymnast swings through two revolutions in 1.90 seconds, we can plug these values into the formula:
ω = (2π * 2) / 1.90
Calculating this expression gives us:
ω = (4π) / 1.90
Now, let's simplify this expression:
ω ≈ 6.64 rad/s
Therefore, the angular velocity of the gymnast is approximately 6.64 rad/s.
To find the angular velocity of the gymnast, we need to use the equation:
Angular velocity = (Final angle - Initial angle) / Time taken
In this case, we are given that the gymnast completes two revolutions on the high bar. A revolution is a complete circle, which is equivalent to 360 degrees or 2π radians.
So, the initial angle is 0 radians, and the final angle is 2π radians (after completing two revolutions).
Given that the time taken is 1.90 seconds, we can substitute these values into the equation:
Angular velocity = (2π radians - 0 radians) / 1.90 seconds
Simplifying the equation gives us:
Angular velocity = (2π radians) / 1.90 seconds
Now, we can calculate the value using a calculator:
Angular velocity ≈ 3.302 radians/second
Therefore, the angular velocity of the gymnast on the high bar is approximately 3.302 radians/second.