An aluminum disk with an inner radius of 2.5cm has a string attached with a hanging mass at the end. The mass of 0.5kg was timed as it fell, rotating the disk. The mass took 4.4s to fall 1.4m. Use the data to determine the moment of inertia for the system.
I don't know where to start.
I don't know where to start.
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using the relation s = 0 + 1/2 a t^2, where 'a' is the tangential acceleration, we can have
1.4 = 0 + 1/2 x a x 4.4 x4.4 ie., a = 0.145 m/sec^
then angular acceleration alpha = a / r = 0.145 / 2.5 x10^-2 = 5.8 rad/sec^2
then moment of inertia I = r^2 m( g-a) / a = 6.25 x10^-4 x 0.5 ( 9.8 - 0.145) / 0.145
= 0.0208 Kg - m^2.
1.4 = 0 + 1/2 x a x 4.4 x4.4 ie., a = 0.145 m/sec^
then angular acceleration alpha = a / r = 0.145 / 2.5 x10^-2 = 5.8 rad/sec^2
then moment of inertia I = r^2 m( g-a) / a = 6.25 x10^-4 x 0.5 ( 9.8 - 0.145) / 0.145
= 0.0208 Kg - m^2.