6. A string is wrapped around a frictionless pulley which has a radius of 3.5 cm. The pulley is initially at rest. A force of 45 N is applied to the string causing the string to unwind without slipping as the pulley rotates. The string unwinds a distance of 1.2 meters in 4.2 seconds. Calculate the rotational inertia of the pulley.7. Astronauts exploring a dwarf planet observe an asteroid approaching the planet on a collision course. When the asteroid is 7520 km away from the center of the planet, its speed is measured to be 148 m/s. Later the asteroid is 2850 km away from the center of the planet and its speed is measured to be 375 m/s. Based on this information, determine the mass of the dwarf planet.11. A 45 cm long rod with a mass of 450 g (m1) has a 700 g mass (m2) attached to the right end. An axle Is fixed through the opposite end of the rod (dot shown at left end). The rod and mass are released from rest In this horizontal position. Calculate the tangential velocity of the mass (m2) as it rotates through its lowest position.12. A 3.0-m-long uniform ladder with a mass of 12 kg leans against a frictionless wall. The ladder Is inclined at an angle of 70" above the floor. The coefficient of static friction between the ladder and the floor is 0.28. A person has left a 25-kg toolbox on a rung 75% of the way up the ladder. a Calculate the force of static friction acting at the bottom of the ladder for the system as shown. b. Will the ladder start to slide? Justify your answer numerically. C. How high up the ladder could the box be placed before the ladder starts sliding