In the arrangement shown in figure a weight A possesses mass m, a pulley B possesses mass M. Also known are the moment of inertia I of the pulley relative to its axis and the radii of the pulley R and `2R`. The mass of the threads is negligible. Find the acceleration of the weight A after the system is set free.

In the arrangement shown in the figure, the blocks have masses 3m,m and 2m , the friction is absent, the masses of the pulleys and the threads are negligible. Find the acceleration of mass 3m .

In the arrangement shown in figure-2.68 the masses of the wedge M and the body m are known. There is no friction at any of the surfaces. The mass of the pulleys and thread is negligible. Find the acceleration of the body m relative to the horizontal surface on which the wedge slides. [(sqrt(2)mg)/(M+2m)]

In the arrangement shown in figure the masses of the wedge M and the body m are known. The appreciable friction exists only between the wedge and the body m , the friction coefficient being equal to k . The masses of the pulley and the thread are negligible. Find the acceleration of the body m relative to the horizontal surface on which the wedge slides.

A pulley fixed to the ceiling carries a thread with bodies of masses m_1 and m_2 attached to its ends. The masses of the pulley and the thread are negligible, friction is absent. Find the acceleration w_C of the centre of inertia of this system.

A pulley fixed to the ceiling carried a thread with bodies of masses m_(1) and m_(2) attached to its ends. The mases of the pulley and the thread are negligible and friction is absent. Find the acceleration of the centre of mass of this system.

In the arrangement shown in figure the bodies have masses m_0 , m_1 , m_2 , the friction is absent, the masses of the pulleys and the threads are negligible. Find the acceleration of the body m_1 . Look into possible cases.

In the arrangement shown in fig the bodies have masses m_(0), m_(1) and m_(2) the friction is absent the masses of pulleys and the threads are negligible find the acceleration of the body m_(1)

In the arrangement shown in figure the masses of the wedge M and the body m are known. The appreciable friction exists only between the wedge and the body m, the friction coefficient being equal to k. The masses of the pulley and the thread are negligible. Find the acceleration of the body m relative to the horizontal surface on which the wedge slides.

Find the frequency of small oscillations of the arrangement illustrated in figure. The radius of the pulley is R , its moment of inertia relative to the rotation axis is I , the mass of the body is m , and the spring stiffness is x .The mass of the thread and the spring is negligible , the thread does not slide over the pulley, there is no friction in the axis of the pulley