A block of 50 kg is attached to a cable. The cable is then attached to a rotating assembly with a mass moment of inertia of 10 kg-m^2. The bearing friction applied at the rotating assembly is equivalent to a couple of 50 N-m CCW. The block's initial downward speed is 1 m/s. 0.5 m 50 kg 3. Which of the following is closest to the work done by the weight of the 50-kg block after the rotating assembly has rotated 0.8 radians CW?

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Two solid spheres of radius R and mass m are initially separated by a distance d such that the two centres of mass are separated by d+3R as shown below. The spheres are initially at rest, but the gravitational force  accelerates them towards each other until they collide.a) Calculate the initial mechanical energy of the system.b) Calculate the gravitational potential energy of the system at the moment they collide.c) Derive an expression for v. State carefully what physical law you are applying.d) Show that, in the limit d >> R, the velocity v is independent of d.

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A hollow sphere rolls without slipping down a ramp that is 3.5 m long. the ramp is inclined at an angle of 20˚ with the horizontal. Use the conservation of energy to find the speed of the sphere at the bottom of the slope if it starts from rest. ( I= 2/3 m R2 )

Please, Do all 3 subparts.

Problem An electric motor provides a constant torque of 12 N.m on a pivoting flywheel which has an inertia around the shaft of 3 kg.m2 and a friction constant of 3 kg.m2 / s. Motor it starts with silence. Zero tolerance is expressed in 2% to face value. 1. Calculate the total work done by the torque from rest until equilibrium is reached angular velocity! 2. Calculate kinetic energy when angular velocity equilibrium is reached! 3. Calculate the average power given by the motor from idle until it is reached equilibrium!

In the figure below, two 8.00 kg blocks are connected by a massless string over a pulley of radius 2.90 cm and rotational inertia 8.00 x 10-4 kg • m2. The string does not slip on the pulley; it is not known whether there is friction between the table and the sliding block; the pulley's axis is frictionless. When this system is released from rest, the pulley turns through 0.150 rad in 60.0 ms, and the acceleration of the blocks is constant. T (a) What is the magnitude of the pulley's angular acceleration? rad/s2 (b) What is the magnitude of either block's acceleration? m/s2 (c) What is the string tension T1? N

The turntable in a microwave oven has a moment of inertia of 0.040 kg⋅m2 and is rotating once every 4.4 s . What is its kinetic energy?Express your answer with the appropriate units.