Let\'s say you were to wrap the fishing line around a larger spindle than the on

Question

Let's say you were to wrap the fishing line around a larger spindle than the one you used in your experiment.  And let's say that you found a hanging mass that fell with the same linear acceleration as the mass you used in you experiment.  Would the angular acceleration of the disc for this setup be larger or smaller than the angular acceleration you measured in your experiment? Explain

my actual angular exceration = 2.112

Diameter of actual spindle used in experiment = 5.03 cm with radius of 2.515cm

mass of actual hanging mass used in experiment = 112.5g

Explanation / Answer

As we know that

Torque = I*alpha = rF

For Disc I = 0.5*m*r^2

Therfore

0.5*m*r^2*alpha = rT

0.5*m*r*alpha = T

alpha = angular acceelration = 2T/(mr) --------------(1)

Also

mg - T = ma

or

mg - T = m*alpha*r

T = m(g - alphar)

Therefore from equation(1) ,we get

alpha = 2*(g/r - alpha)

alpha = (2/3)*(g/r)

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