a stone attached to the end of elastic string is whirled around in a circular path of radius 20cm if the stone makes 15 complete revolution in 5 seconds, calculate its angular and linear velocities.
I don't know the answer
ω = 15rev/5sec = 3rev/s = 6π rad/s
v = 20*2π cm/rev * 3rev/s = 120π cm/s
What's the answer with it's calculations
To calculate the angular and linear velocities of the stone, we need to use the formula:
Angular velocity (ω) = 2π * frequency (f)
Linear velocity (v) = ω * radius (r)
First, let's calculate the frequency. The stone completes 15 revolutions in 5 seconds, so the frequency (f) can be calculated as:
Frequency (f) = Number of revolutions / Time
= 15 / 5
= 3 Hz
Next, we can use the formula for angular velocity to calculate ω:
Angular velocity (ω) = 2π * frequency (f)
= 2π * 3
= 6π rad/s
Now, we can use the formula for linear velocity to calculate v:
Linear velocity (v) = ω * radius (r)
= 6π * 20 cm/s
= 120π cm/s
So, the angular velocity of the stone is 6π rad/s, and the linear velocity is 120π cm/s.