Exam 11: Motion in a Circle

If an object travels at a constant speed in a circular path,the acceleration of the object is

A piece of thin uniform wire of mass m and length 3b is bent into an equilateral triangle.Find the moment of inertia of the wire triangle about an axis perpendicular to the plane of the triangle and passing through one of its vertices.

A 1.25-kg ball begins rolling from rest with constant angular acceleration down a hill.If it takes 3.60 s for it to make the first complete revolution,how long will it take to make the next complete revolution?

A disk-shaped space station 175 m in diameter spins uniformly about an axis perpendicular to the plane of the disk through its center.How many rpm (rev/min)must this disk make so that the acceleration of all points on its rim is g/2?

A turntable has a radius of 0.80 m and a moment of inertia of 2.0 kg • m².The turntable is rotating with an angular velocity of 1.5 rad/s about a vertical axis though its center on frictionless bearings.A very small 0.40-kg ball is projected horizontally toward the turntable axis with a velocity of 3.0 m/s.The ball is caught by a very small and very light cup-shaped mechanism on the rim of the turntable (see figure).The percent of the initial kinetic energy of the system that is lost during the capture of the ball is closest to

A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg • m² is rotating freely with an angular speed of 1.0 rad/s.Two people,each having a mass of 60 kg,are standing right outside the edge of the merry-go-round and step on it with negligible speed.What is the angular speed of the merry-go-round right after the two people have stepped on?

A 1000-kg car is slowly picking up speed as it goes around a horizontal curve whose radius is 100 m.The coefficient of static friction between the tires and the road is 0.350.At what speed will the car begin to skid sideways?

A 1.15-kg grinding wheel 22.0 cm in diameter is spinning counterclockwise at a rate of 20.0 revolutions per second. When the power to the grinder is turned off,the grinding wheel slows with constant angular acceleration and takes 80.0 s to come to a rest. (a)What was the angular acceleration (in rad/s²)of the grinding wheel as it came to rest if we take a counterclockwise rotation as positive? (b)How many revolutions did the wheel make during the time it was coming to rest?

A bicycle is traveling north at 5.0 m/s.The mass of the wheel,2.0 kg,is uniformly distributed along the rim,which has a radius of 20 cm.What are the magnitude and direction of the angular momentum of the wheel about its axle?

A record is dropped vertically onto a freely rotating (undriven)turntable.Frictional forces act to bring the record and turntable to a common angular speed.If the rotational inertia of the record is 0.54 times that of the turntable,what percentage of the initial kinetic energy is lost?

A car drives over a hilltop that has a radius of curvature 0.120 km at the top of the hill. At what speed would the car be traveling when it tires just barely lose contact with the road when the car is at the top of the hill?

A slender uniform rod 100.00 cm long is used as a meter stick.Two parallel axes that are perpendicular to the rod are considered.The first axis passes through the 50-cm mark and the second axis passes through the 30-cm mark.What is the ratio of the moment of inertia through the second axis to the moment of inertia through the first axis?

A string is attached to the rear-view mirror of a car.A ball is hanging at the other end of the string.The car is driving around in a circle,at a constant speed.Which of the following lists gives all of the forces directly acting on the ball?

A Ferris wheel has diameter of 10 m and makes one revolution in 8.0 seconds.A person weighing 670 N is sitting on one of the benches attached at the rim of the wheel.What is the apparent weight (that is,the normal force exerted on her by the bench)of the person as she passes through the highest point of her motion?

A ball is tied to the end of a cable of negligible mass. The ball is spun in a circle with a radius 2.00 m making 7.00 revolutions every 10.0 seconds. What is the magnitude of the acceleration of the ball?

A dumbbell-shaped object is composed by two equal masses,m,connected by a rod of negligible mass and length r.If I₁ is the moment of inertia of this object with respect to an axis passing through the center of the rod and perpendicular to it and I₂ is the moment of inertia with respect to an axis passing through one of the masses,it follows that

While spinning down from 500.0 rpm to rest,a solid uniform flywheel does 5.1 kJ of work.If the radius of the disk is 1.2 m,what is its mass?

A wind farm generator uses a two-bladed propeller (see figure)mounted on a pylon at a height of 20 m.The length of each propeller blade is 12 m.A small piece from the tip of the propeller breaks off when the propeller is vertical.At that instant,the period of the motion of the propeller is 1.2 s.The fragment flies off horizontally,falls with negligible air resistance,and strikes the ground at P. (a) How far is point P from the base of the pylon? (b) At what angle with respect to the vertical is the fragment moving just as it strikes the ground at P?

A 4.50-kg wheel that is 34.5 cm in diameter rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 13.5 rad/s.What is the magnitude of the angular acceleration of the wheel?

A 23 kg mass is connected to a nail on a frictionless table by a massless string 1.3 m long.There is no appreciable friction between the nail and the string.If the tension in the string is 51 N while the mass moves in a uniform circle on the table,how long does it take for the mass to make one complete revolution?