While fishing, you get bored and start to swing a sinker weight around in a circle below you on a 0.50 piece of fishing line. The weight makes a complete circle every 0.40 .
To calculate the speed of the sinker weight as it swings around in a circle, you need to find its angular velocity. The angular velocity is the rate at which an object rotates or moves in a circular path.
In this case, you know that the sinker weight completes one full circle every 0.40 seconds. To find the angular velocity, you need to divide the angle of the circle (2π radians) by the time it takes to complete one circle.
Angular velocity (ω) = 2π radians / Time (T)
Given:
Angle (θ) = 2π radians
Time (T) = 0.40 seconds
Substituting the values into the formula:
Angular velocity (ω) = 2π radians / 0.40 seconds
Now, let's calculate the angular velocity:
ω = 6.28 radians / 0.40 seconds
ω ≈ 15.7 radians/second
Therefore, the sinker weight has an angular velocity of approximately 15.7 radians/second as it swings around in a circle.