A hanger of mass m is attached to a lightstring that is wrapped around the rim o

Question

A hanger of mass m is attached to a lightstring that is wrapped around the rim of a wheel of radiusr. The wheel is released, allowing the weight to fall andcause the wheel to accelerate rotationally. In the experiment, therotational acceleration is measured. Theacceleration of gravity is g (defined as a positivequantity), and the moment of inertia is I. Work out aformula for I by following the stteps given below.

All answers are formulas, and should contain only symbols from thefollowing set: hanger mass m (type "m"), acceleration ofgravity g (type "g"), moment of inertia I (type"I"), radius r (type "r"), linear acceleration of thefalling weight a (type "a"), string tension T(type "T"), and rotational acceleration (type"alpha"). Use the previewer ("eye" icon) to check the formatting ofyour answer before you submit it. Check this link for help onentering formulas:

Explanation / Answer

1. T - mg = ma 2. Tr = -Ia/r 3. a = -mg/((I/r^2) + m) 4. I = (((mg)/(ralpha)) - m)r^2

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