A stopper tied to the end of a string is swung in a horizontal circle. If the mass of the stopper is 13.0 g, and the string is 93.0 cm, and the stopper revolves at a constant speed 10 times in 11.8 s,
a. What is the angular velocity of the stopper?
it goes 2PI*10 radians in 11.8 seconds.
w=20PI/11.8 rad/sec
To find the angular velocity of the stopper, we need to use the formula:
Angular velocity (ω) = 2π * frequency
First, let's find the frequency. We are given that the stopper revolves at a constant speed of 10 times in 11.8 seconds. Therefore, the frequency can be calculated as:
Frequency (f) = number of revolutions / time
In this case, the number of revolutions is 10 and the time is 11.8 seconds. So:
Frequency (f) = 10 / 11.8
Now we can find the angular velocity using the formula:
Angular velocity (ω) = 2π * frequency
Angular velocity (ω) = 2π * (10 / 11.8)
Substituting the numerical values:
Angular velocity (ω) ≈ 2π * (0.847)
Evaluating the expression:
Angular velocity (ω) ≈ 5.33 rad/s
Therefore, the angular velocity of the stopper is approximately 5.33 rad/s.