A massless string is wrapped around a cylinder of mass 0.400 kg and radius 0.100

Question

A massless string is wrapped around a cylinder of mass 0.400 kg and radius 0.100 m. The string is attached to the ceiling. The cylinder is released. As it falls, the string unwinds. What is the magnitude of the acceleration of the cylinder as it falls in m/s2?

A massless string is wrapped around a cylinder of mass 0.400 kg and radius 0.100 m. The string is attached to the ceiling. The cylinder is released. As it falls, the string unwinds. What is the magnitude of the acceleration of the cylinder as it falls in m/s2?

Explanation / Answer

mg-T=ma

T*r=I = (mr^2/2)*

=>T*0.1 = 0.4*(0.1)^2/2*a/0.1

=>T=0.2a

=>0.4*9.8 - 0.2a = 0.4a

=>a = 6.53 m/s^2

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