Answer: 2.75 1/sec
Explanation:
The only external force (neglecting gravity) acting on the puck, is the centripetal force, which. in this case, is represented by the tension in the string, so we can say:
T = mv² / r (1)
Our unknown, is the frequency at which the puck can go around the circle, which is the inverse of the period Tp.
By definition, a period is the time needed by the puck to complete one entire circle.
By definition also , angular velocity is the rate of change of the angle advanced, so we can express this way:
ω = ∆θ / ∆t
The angle advanced during one period, is exactly (by angle definition) 2 π radians.
So, we can always write the angular velocity, ω, as follows:
ω = 2π / Tp = 2πf
Now, there is a relationship between linear and angular velocity, that can be found applying simply the definition of velocity and of an angle too, as follows:
v = ∆s / ∆t = r ∆θ/∆t = ω r
Replacing in (1), we have:
T = mω2 r2 / r = m ω2r (2)
We have just found that ω= 2πf, so, replacing in (2) :
T = m (2π)2 f2 r
Solving for f:
f = 1/2π√(T/mr) = 1/2π 17.28 1/sec = 2.75 1/sec
