Assignment:1.)A wheel free to rotate about its axis that is not frictionless is initially at rest. A constant external torque of +50 N·m is applied to the wheel for 21 s, giving the wheel an angular velocity of +650 rev/min. The external torque is then removed, and the wheel comes to rest 120 s later. (Include the sign in your answers.)(a) Find the moment of inertia of the wheel.(b) Find the frictional torque, which is assumed to be constant.2.)You set out to design a car that uses the energy stored in a flywheel consisting of a uniform 92-kg cylinder of radius R that has a maximum angular speed of 330 rev/s. The flywheel must deliver an average of 2.30 MJ of energy for each kilometer of distance. Find the smallest value of R for which the car can travel 300 km without the flywheel needing to be recharged.3.)A 0.27 kg rod of length 95 cm is suspended by a frictionless pivot at one end. It is held horizontal and released.(a) Immediately after it is released, what is the acceleration of the center of the rod?(b) Find the initial acceleration of a point on the end of the rod.(c) What is the linear velocity of the center of mass of the rod when it is vertical?4.)A park merry-go-round consists of a 210 kg circular wooden platform 3.90 m in diameter. Four children running alongside push tangentially along the platform’s circumference until, starting from rest, the merry-go-round reaches a steady speed of one complete revolution every 2.8 s. (a) If each child exerts a force of 26 N, how far does each child run?(b) What is the angular acceleration of the merry-go-round?(c) How much work does each child do?(d) What is the kinetic energy of the merry-go-round?5.)The roof of the student dining hall at your college will be supported by high cross-braced wooden beams attached in the shape of an upside-down L. Each vertical beam is 10.0 ft high and 2.0 ft wide, and the horizontal cross-member is 8.0 ft long. The mass of the vertical beam is 322.0 kg, and the mass of the horizontal beam is 271.6 kg. As the workers were building the hall, one of these structures started to fall over before it was anchored into place. (Luckily they stopped it before it fell.) (a) If it started falling from an upright position, what was the initial angular acceleration of the structure? Assume that the bottom did not slide across the floor and that it did not fall out of plane; that is, during the fall, the structure remained in the vertical plane defined by the initial position of the structure.(b) What would be the magnitude of the initial linear acceleration of the upper right corner of the horizontal beam?(c) What would the horizontal component of the initial linear acceleration be at this same location?(d) Estimate the structure’s rotational speed at impact.
