The acceleration of the mass down the plane is determined as (4mg sinθ)/(3mr²).
Conservation of angular momentum
The acceleration of the mass down the plane is determined by applying the principle of conservation of angular momentum.
Fr = Iα
where;
- F is weight of the object parallel to the plane
- r is the radius of the flywheel
- I is moment of inertia
- α is angular acceleration
(mg sinθ)r = Iα
(mg sinθ)r = I(ar)
(mg sinθ) = I(a)
[tex]a = \frac{mg \times sin(\theta)}{I} \\\\a = \frac{mg \times sin(\theta)}{3mr^2/4} \\\\a = \frac{4mg \times sin(\theta)}{3mr^2}[/tex]
Thus, the acceleration of the mass down the plane is determined as (4mg sinθ)/(3mr²).
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