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Exam 8: Rotational Equilibrium and Dynamics

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Question 31

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A bucket of water with total mass 24.0 kg is attached to a rope,which in turn,is wound around a 0.050-m radius cylinder at the top of a well.A crank with a turning radius of 0.35 m is attached to the end of the cylinder.What minimum force directed perpendicular to the crank handle is required to just raise the bucket? (Assume the rope's mass is negligible,that the cylinder turns on frictionless bearings,and that g = 9.8 m/s². )

A) 1 600 N
B) 3.4 N
C) 34 N
D) 670 N
E) 4.1 N

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Question 32

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An object consists of a rod (of length 3.00 m and negligible moment of inertia) to which four small 3.50-kg masses are attached,one at each end and one at each point on the rod spaced at 1.00-m intervals.The moment of inertia of this object about an axis perpendicular to the rod and through one of the end masses:

A) is 49 kg·m².
B) is 21 kg·m².
C) is 31.5 kg·m².
D) is 10.5 kg·m².
E) cannot be uniquely determined until it is stated which inner mass the axis goes through.

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Question 33

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A ventilation fan with a moment of inertia of 0.040 kg·m² has a net torque of 0.160 N·m applied to it.What angular acceleration does it experience?

A ventilation fan with a moment of inertia of 0.034 kg·m² has a net torque of 0.11 N·m applied to it.If it starts from rest,what angular momentum will it have 9.0 s later?

A solid sphere,a solid cylinder,and a hoop each have the same mass and radius.If they are spinning at the same angular velocity,which one has the greatest rotational kinetic energy?

A bucket of water with total mass 20.0 kg is attached to a rope,which in turn is wound around a 4.00-cm radius cylinder at the top of a well.The bucket is raised to the top of the well and released.The bucket is moving with a speed of 8.00 m/s upon hitting the water surface in the well.What is the angular speed of the cylinder at this instant?

A hoop with mass,M,and radius,R,rolls along a level surface without slipping with a linear speed,v.What is the ratio of rotational to linear kinetic energy? (For a hoop,I = MR². )

A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape.Each baton was 0.70 m long and each ball on the end is 0.10 kg.(Ignore the mass of the rods. ) What is the moment of inertia if the arrangement is spun around an axis through the center perpendicular to both rods?

A solid sphere of mass 2.50 kg and radius 0.120 m starts from rest at the top of a ramp inclined 15.0° and rolls to the bottom.The upper end of the ramp is 1.60 m higher than the lower end.What is the linear speed of the sphere when it reaches the bottom of the ramp? (Note: I = MR² for a solid sphere,and g = 9.80 m/s². )

A bowling ball has a mass of 7.00 kg,a moment of inertia of 2.8 × 10−² kg·m²,and a radius of 0.100 m.If it rolls down the lane without slipping at a linear speed of 4.30 m/s,what is its angular speed?

An astronaut is on a 100-m lifeline outside a spaceship,circling the ship with an angular speed of 0.100 rad/s.How far inward can she be pulled before the centripetal acceleration reaches 4g = 39.2 m/s²?

A solid cylinder of mass 3.0 kg and radius 0.2 m starts from rest at the top of a ramp,inclined 15°,and rolls to the bottom without slipping.(For a cylinder I = MR². ) The upper end of the ramp is 1.5 m higher than the lower end.Find the linear speed of the cylinder when it reaches the bottom of the ramp.(g = 9.8 m/s²)

If a nonzero torque is applied to an object,that object will experience:

A 5.0-kg mass is placed at (3.0,4.0) m,and a 6.0-kg mass is placed at (3.0,−4.0) m.What is the moment of inertia of this system of masses about the x axis?

A cylinder with its mass concentrated toward the center has a moment of inertia of 0.2MR².If this cylinder is rolling without slipping along a level surface with a linear speed v,what is the ratio of its rotational kinetic energy to its linear kinetic energy?

A rod of length L is hinged at one end.The moment of inertia as the rod rotates around that hinge is ML²/3.Suppose a 2.00-m rod with a mass of 6.00 kg is hinged at one end and is held in a horizontal position.The rod is released as the free end is allowed to fall.What is the angular acceleration as it is released?

An 8.4-kg mass is placed at (3.0,4.0) m.Where can a 4.2-kg mass be placed so that the moment of inertia about the z axis is zero?

A tetherball is attached to a pole with a 2.0-m rope.It is circling at 0.20 rev/s.As the rope wraps around the pole,it shortens.How long is the rope when the ball is moving at 6.0 m/s?

A bowling ball has a mass of 7.00 kg,a moment of inertia of 2.80 × 10−² kg·m²,and a radius of 0.100 m.If it rolls down the lane without slipping at a linear speed of 4.00 m/s,what is its total kinetic energy?

The Earth's density increases with depth.If instead the Earth had uniform density,but the same angular velocity and mass,how would its rotational kinetic energy compare to the actual value?