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lubasha [3.4K]
3 years ago
13

A wheel at rest gains an angular momentum of 10.7kgm²/s in 8s. if the moment if inertia of the wheel is 2.2kgm², how many revolu

tions will be made before the wheel attains an angular velocity of 30rad/s
​
Physics
1 answer:
EleoNora [17]3 years ago
3 0

Answer:

Revolutions made before attaining angular velocity of 30 rad/s:

θ = 3.92 revolutions

Explanation:

Given that:

L(final) = 10.7 kgm²/s

L(initial) = 0

time = 8s

<h3>Find Torque:</h3>

Torque is the rate of change of angular momentum:

T = \frac{L(final)-L(initial)}{t}\\T = \frac{10.7-0}{8}\\T=1.34 Nm

<h3>Find Angular Acceleration:</h3>

We know that

T = Iα

α = T/I

where I = moment of inertia = 2.2kgm²

α = 1.34/2.2

α = 0.61 rad/s²

<h3>Find Time 't'</h3>

We know that angular equation of motion is:

ω²(final) = ω²(initial) +2αθ

(30 rad/s)² = 0 + 2(0.61 rad/s²)θ

θ = (30 rad/s)²/ 2(0.61 rad/s²)

θ = 24.6 radians

Convert it into revolutions:

θ = 24.6/ 2π

θ = 3.92 revolutions

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\frac{r_1}{r_2}=6.9

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