The figure below shows, at left, a solid disk of radius R = 0.600 m and mass 75.0 kg. Mounted directly to it and coaxial with it is a pulley with a much smaller mass and a radius of r= 0.230 m. The disk and pulley assembly are on a frictionless axle. A belt is wrapped around the pulley and connected to an electric motor as shown on the right. The turning motor gives the disk and pulley a clockwise angular acceleration of 1.67 rad/s?. The tension T,, in the upper (taut) segment of the belt is 165 N. (a) What is the tension (in N) in the lower (slack) segment of the belt? (b) What If? You replace the belt with a different one (one slightly longer and looser, but still tight enough that it does not sag). You again turn on the motor so that the disk accelerates clockwise. The upper segment of the belt once again has a tension of 165 N, but now the tension in the lower belt is exactly zero. What is the magnitude of the angular acceleration (in rad/s?)? rad/s2

A pulley with moment of inertia I = 0.75 kg-m² and radius R = 15 cm is mounted on a wall. A light string is wrapped around the pulley with a mass m = 2.0 kg attached to the end. The pulley rotates as the mass falls. Use Newton's second law to calculate the acceleration of the mass. Check that your formula gives the expected behavior when I →0. => To help get started, the free body diagrams m and the pulley is shown below. T m Write down Newton's second law for each diagram. Use (and explain) the relationship R a = RO TIL R T

Three objects are spinning as shown in the figure. Each object has a total mass of m and a radius of R. The object on the left is a hoop with its mass evenly distributed around the rim. The object in the middle is a solid sphere with its mass evenly distributed throughout. The object on the right consists of a massless rod 2R long with a point mass of 0.5m attached to each end. Which object has the greatest moment of inertia and which one the least? Mass m Mass = m Mass = 0.5m The rod + masses is the largest; the hoop is the smallest The sphere is the largest, the hoop is the smallest The hoop is the largest; the rod + masses is the smallest The hoop is the largest; the sphere is the smallest The rod + masses is the largest; the sphere is the smallest

The block on the right has a mass of M = 4.2 kg, see the figure below. It takes 2.9 s to reach the floor after beingreleased from rest. What then is the mass of the block on the left (m)? Assume the string is massless, but the pulley has amass of 3.9 kg and a radius of 14 cm.