Question

A ball of mass 200 g is on one end of a string of length 20 cm, It is revolved in a horizontal circle at a angular frequency of 6 rpm, then it's angular velocity

Please help me! It's quite urgent!
Points - 50

Answer 1

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 2

Hey there,

Number of rotations per unit time give us the frequency and the time taken for one rotation give the time period.

Since frequency=6 rotations per minute
Hence we can use unitary method to get--

6 rotations----1 minute
6 rotations----60 seconds
6/60 rotations----1 second
Hence the frequency-
υ(nu)=0.1 Hertz

According to formula,
Angular velocity(ω) is given by-
ω=2πυ
ω=2π*0.1 radians per second
=0.2π radians per second

For conversion to SI unit, we get 1 radian = π/180 degrees
0.2 radians = π/900 degrees
Hence 0.2π radians = π²/900 degrees

So we get,
SI angular velocity=(π²/900)° per second

Hope it helps>>>

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