What is the moment of inertia of an object that rolls without slipping down a 2.00-m-high incline starting from rest, and has a final velocity of 6.00 m/s? Express the moment of inertia as a multip ? le of ?MR2, where ? M is the mass of the obj? ect and ?R is its radius.
Step-by-step solution Step 1 of 1 The moment of inertia of an object rolling down an incline, starting from rest and having a final velocity is calculated from the energy conservation method as, Here, is the kinetic energy of the object before it starts to roll down, is the gravitational potential energy of the object on the top of the incline, is the kinetic energy of the objects when it comes down the incline and is the gravitational potential energy at the bottom. Substitute 0 for , for , + for and 0 for , Here, is the mass of the object, is the gravitational acceleration, is the moment of inertia of the object, is the angular velocity of the object, is the height of the incline and is the linear velocity of the object. Substitute for , 9. 8 m/s2 for and 6 m/s for V . So, the moment of inertia is .