A wheel of radius R, mass M and moment of inertia I is mounted on a frictionless axle.A light cord is wrapped around the wheel and attached to a block of mass m. Calculate the angular acceleration...

A wheel of radius R, mass M and moment of inertia I is mounted on a

frictionless axle.

A light cord is wrapped around the wheel and attached to a block of mass m. Calculate the angular acceleration of the wheel.

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Posted on

Moment of inertia of a wheel is given by;

`I = m*R^2`

The torque applied on the chord is due to the weight of mass m as the tension of chord.

Where g is the gravitational accelaration.

But we know that `tau = I*alpha`

Where `alpha` is the angular accelaration.

 

Torque `tau = R*T = R*mg`

So `R*mg`=`I*alpha`

`alpha = R*(mg)/I` =`(R*mg)/(MR^2)`` =((mg)/(MR))`

 

So angular accelaration is (mg/MR)

 

Sources:

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