A cyclist completes 3.2 cycle revolutions in 1.4s. What is the angular velocity in radians per second?

one rotation is 2pi radians.

So the cyclist does 3.2(2pi)/1.4 radians/s
= 14.36 radians/s

To find the angular velocity in radians per second, we can use the formula:

Angular Velocity (ω) = (Total Angle Covered)/(Time Taken)

We can find the total angle covered by the cyclist by multiplying the number of cycle revolutions by 2π (the number of radians in one revolution).

Total Angle Covered = (3.2 revolutions) * (2π radians/revolution)

Total Angle Covered = 6.4π radians

Now, we can substitute the values to find the angular velocity:

ω = (6.4π radians) / (1.4 seconds)

Simplifying the expression gives:

ω ≈ 14.454 radians per second

Therefore, the angular velocity is approximately 14.454 radians per second.

To find the angular velocity in radians per second, we need to know the number of radians covered in a given time period.

The formula to calculate angular velocity is:

Angular Velocity (in radians per second) = (Number of Radians Covered) / (Time Taken)

We are given that the cyclist completes 3.2 cycle revolutions in 1.4 seconds.

To find the number of radians covered, we need to convert the cycle revolutions to radians.

One cycle revolution is equal to 2π radians. Therefore:

Number of Radians Covered = 3.2 (Cycle Revolutions) * 2π (radians per cycle revolution)

Now we can substitute the values into the formula:

Angular Velocity (in radians per second) = (3.2 * 2π) / 1.4

To calculate the angular velocity, we multiply 3.2 by 2π and then divide by 1.4.

Finally, we can simplify the expression and calculate the answer:

Angular Velocity (in radians per second) ≈ 14.37 radians per second