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?
angular velocity? 2PI*10/11.8 rad/sec
To find the angular velocity of the stopper, we can use the formula:
Angular velocity (ω) = 2π * f
where ω is the angular velocity in radians per second and f is the frequency of the revolution in hertz (Hz).
To find the frequency (f), we can use the formula:
f = 1 / T
where f is the frequency in Hz and T is the period of revolution in seconds.
Given that the stopper revolves 10 times in 11.8 seconds, we can calculate the period as:
T = 11.8 s / 10
T = 1.18 s
Now we can calculate the frequency:
f = 1 / 1.18 s
f ≈ 0.847 Hz
Finally, we can calculate the angular velocity:
ω = 2π * 0.847 Hz
ω ≈ 5.32 rad/s
Therefore, the angular velocity of the stopper is approximately 5.32 radians per second.