A ball of mass 200g is on one end of a string of length 20cm. It is revolved in a horizontal circle at a
angular frequency of 6 rpm the angular velocity is.
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Explanation:
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Frequency = f = 6 rpm = 6/60 = 0.10 rotations/sec.
rpm = rotations per minute.
Angular velocity ω = 2 π f (because each rotation an angle of 2π is covered. there are f rotations per sec.).
ω = 2 π * 0.10 = 0.2 π rad/sec.
========= Other quantities...
(ω = 2π/T, as T=1/f = time period)
m = 0.200 kg. L = 0.20 m.
Linear velocity (along tangent to circle) = v = L ω = 0.20 * 0.2π = 0.04π m/s
Centripetal force = m v²/L = 0.200 * 0.04² π²/0.20 N
Tension force in the string = Centripetal force.
KE = 1/2 m v² = 1/2 * 0.200 * 0.04² π² J
Answer:
Radius of the circle =0.2 m
Angular frequency =n=6rpm
w=
60 s
6×2π
w=
5
π
=0.6284 rad/s
Linear velocity of the ball =rw
v=0.2 m×0.628 m/s
v=0.1257 m/s