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A microwave oven has a rotating plate 30 cm in diameter. From rest the plate accelerates at a uniform 2 rate of 0.87 rad/s for 0.5 s. a. How many revolutions does the plate make before reaching operational speed? b. What are the angular and tangential speeds of the object at the rim? A small coin is placed on a turntable that makes 3 revolutions in 3.14 s. What is the speed of the coin when it rides 5 cm away from the center? If the mass of the coin is 2 g, what is the frictional force acting on it? If the coin slides off when it is placed 10 cm away from the center, what is μs? A CD accelerates uniformly from rest to operational speed of 500 RPM (revolutions per minute) in 3.5 s. What is the angular acceleration of the CD? If the CD comes to a rest 4.5 s, what is the angular acceleration? How many revolutions occur during this time? The object is pivoted at A and two forces act on it as shown. If r1= 1.3 m and r2 = 2.15 m, F1= 4.2 N and F2 = 4.9 N, θ1= 75° and θ2 = 60°, what is the net torque?F F 1 θ1 r θ2 A r 2 Tracy is building a mobile. Equilibrium: mobile She hangs a 0.02 kg sailboat 0.1 m from the left end and a 0.015 kg truck 0.2 m from the right end of a bar 0.5 m long. Where must the support string be placed such that it is balanced? A beam of length L, whose mass is 1.8 kg rests w/ its ends on 2 digital scales. A block w/ M = 2.7 kg rests on the beam a distance ¼ L from the beam’s left end. What do the two scales read? Equilibrium: board on 2 scales scale scale ¼L L Bob the window washer is Equilibrium: window washers standing on a hanging scaffold supported by a vertical rope at each end. The scaffold weighs 205 N and is 3 m long. What is the force each rope exerts on the scaffold when a 675 N Bob stands 1 m from the right A ladder ml = 15 kg rest against a smooth wall (frictionless). Paul the painter with mp = 78 kg stands on the ladder. What frictional force must act on the ladder 5.6 m to keep it 1m from slipping? 1.6 m Ex: A toy consisting of two balls, each 0.45 kg at the ends of a 0.46 m long, thin, lightweight rod is shown. Find the moment of inertia of the toy about the center of the rod. Each sphere has a mass of 0.1 kg. The distance between each sphere is 0.2 m. Find the moment of inertia if the rotation is about A. About B? A B C Consider the following solid cylinder with two forces acting on it. If the mass of the cylinder is 50 kg, determine the 100 N 80 N angular 12 cm acceleration produced by 8 cm the two forces. If the radius of a basketball is 12 cm and the mass is 0.6 kg, determine the angular acceleration of the ball if it rolls down an incline of 5 degrees. How far does the ball roll in 1.4 seconds? A 2 kg sphere with a radius of 25 cm rolls (without slipping) down an inclined plane of height 0.3 m and length 0.5 m. Determine the linear speed of the cylinder’s center of mass when it reaches the bottom of the incline. A block with a mass of m = 5 kg is hung from a pulley of radius 15 cm and a mass M = 8 kg and then released from rest. What is the speed of the block as it strikes the floor 2 m below its initial position? What is the rotational kinetic energy of the pulley just before the block strikes the floor? At what rate was work done on the pulley? Ex: A child of mass m = 30 kg stands at the edge of a small merry-go-round that’s rotating at a rate of 1 rad/s. The merry-go-round is a disk of radius R = 2.5 m and a mass of M = 100 kg. If the child walks in, toward the center of the disk and stops 0.5 m from the center, what will happen to the angular velocity of the merry-go-round (neglect an effects due to friction)? A student sits on a rotating stool holding two 3 kg masses. When his arms are extended horizontally the masses are 1 m from the axis of rotation. He rotates with angular speed of 0.75 rad/s, and the moment of inertia of the student-stool is 3 2 kgm . The student then pulls the masses to 0.3 m, what is the new angular speed? A 55 kg person stands at the edge of a 6.5 m diameter turntable that has a moment of inertia of 1700 kgm2. The turntable is stationary until the person begins running on the turntable w/ a v = 3.8 m/s. What is the angular velocity of the turntable?