a mass of 5 kg is moving 300 rpm in circle in circle of radius of 1m its kinetic energy will be
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Step by step explanations :
Here, m=5kg,r=1m
ω=30060rps=5rps=5×2πrads−1ω=30060rps
=5rps
=5×2πrads-1
K.E.=12mυ2=12m(rω)2=12×5(1×10π)2=250π2J
Answered by
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Given:
m = 5 kg
f = 300 rpm
R = 1 m
To Find:
The kinetic energy of the given mass.
Calculation:
- Frequency = 300 rpm
⇒ f = 300/60 rps = 5 rps
- The angular velocity is calculated as:
ω = 2πf = 2π × 5
⇒ ω = 10π rad/s
- The linear velocity is calculated as:
v = Rω = 1 × 10π
⇒ v = 10π m/s
- Putting the value of mass and velocity in the formula of KE, we get:
KE = (1/2)mv²
⇒ KE = (1/2) × 5 × (10π)²
⇒ KE = 250π² J
or KE = 250 × (3.14)²
⇒ KE = 2465 J
-So, the Kinetic Energy of the given mass in the circular motion is 2465 J (or 250π² J).
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