A mass of .375kg hangs from a string that is wrappedaround disk with a radius of

Question

A mass of .375kg hangs from a string that is wrappedaround disk with a radius of .26m. When the mass isreleased, the mass accelerates downward at 5.67m/s^2 and thepulley rotates about its axis as the string unwinds. What is themoment of inertia. What I did was use the equation = I. So my torque was the mass* acceleration and my angularacceleration was acceleration divided by the radius. I divided my by but that was incorrect. Where am I goingwrong? A mass of .375kg hangs from a string that is wrappedaround disk with a radius of .26m. When the mass isreleased, the mass accelerates downward at 5.67m/s^2 and thepulley rotates about its axis as the string unwinds. What is themoment of inertia. What I did was use the equation = I. So my torque was the mass* acceleration and my angularacceleration was acceleration divided by the radius. I divided my by but that was incorrect. Where am I goingwrong? What I did was use the equation = I. So my torque was the mass* acceleration and my angularacceleration was acceleration divided by the radius. I divided my by but that was incorrect. Where am I goingwrong?

Explanation / Answer

Given that the mass is M = 0.375kg           radiusis R = 0.26m            accelarationis a = 5.67 m/s2----------------------------------------------------------------------------------                                          Apply Newtons laws forthe mass and the pully then                            Mg - T =Ma              (for mass M)      -----------(1)                                           T*R=I              (for pully)                                    T*R = Ia/R                                         T = Ia/R2       ---------(2)           From the equations (1) and (2) we get                               Mg - Ia/R2 = Ma                                  where I   is the moment of inertia of the solidcylinder                                           I = (Mg- Ma)R2/a                              =--------- kg.m2        Apply Newtons laws forthe mass and the pully then                            Mg - T =Ma              (for mass M)      -----------(1)                                           T*R=I              (for pully)                                    T*R = Ia/R                                         T = Ia/R2       ---------(2)           From the equations (1) and (2) we get                               Mg - Ia/R2 = Ma                                  where I   is the moment of inertia of the solidcylinder                                           I = (Mg- Ma)R2/a                              =--------- kg.m2

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