A paper cutter is made of a uniform bar attached by its lower end to a horizontal base by a frictionless axle. The bar of mass m_b and length l_b is initially at rest and perpendicular to the base. When the bar is barely moved from its initial position it rotates around the axle. Determine the expression of the angular velocity at the instant the bar strikes the base.

A pole-like structure measuring 1.80 m in length stands upright and begins to fall, with its bottom end fixed in place. Applying the principle of conservation of energy determine the speed that the upper end of the structure attains just before it reaches the ground.

A rollerblader moves downhill on an inclined plane with an initial velocity equal to 9.0 m/s. Suddenly one wheel weighing around 0.12 kg got detached while he was still 65 m above ground level. This wheel can be modeled as a thin cylinder with a diameter equal to 60 cm ignoring any other attachments on it. What will be the total kinetic energy of this wheel once it hits ground level?

A solid disk with a diameter of 12 cm and mass of 6.0 × 10² g starts from rest at the top of an inclined plane that has a length of 4.0 m along the incline and an angle of 35° with the horizontal. Calculate its angular speed when it rolls down to the base. Assume that it rolls without slipping.

Two spherical balls of masses m₁ = 32.0 kg and m₂ = 45 kg are linked by a thread which is passed over a cylindrical pulley of radius r = 0.422 m and mass 2.5 kg. The system is initially held still in such a state that m₁ is on the floor while m₂ is at a height of 4.2 m above the floor. Using the principle of conservation of energy, calculate the speed of m₂ just when it hits the floor after the system is released. Assume that there is no friction.