The same force is applied to two hoops. The hoops have the same mass, but the larger hoop has twice the radius. How are the angular accelerations of the hoops related

The angular accelerations of the hoops are related by the following equation .

Explanation:

Net force on the hoop is given by;

where;

a is linear acceleration

m is the mass

Net torque on the hoop is given by;

where;

I is moment of inertia

α is the angular acceleration

But, τ = Fr

let the angular acceleration of the smaller hoop = α₁

let the radius of the smaller hoop = r₁

then, the radius of the larger loop, r₂ = 2r₁

let the angular acceleration of the larger hoop = α₂

Therefore, the angular accelerations of the hoops are related by the following equation

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