Exam 8: Rotational Equilibrium and Rotational Dynamics: Part A

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A 4.0-kg mass is placed at (3.0,4.0)m,and a 7.0-kg mass is placed at (3.0,−4.0)m.What is the moment of inertia of this system of masses about the y axis?

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Tasha has mass 20 kg and wants to use a 6.0-m board of mass 10 kg as a seesaw.Her friends are busy,so Tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board.How far is she from the support point?

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A ventilation fan with a moment of inertia of 0.034 kg·m2 has a net torque of 0.14 N·m applied to it.What angular acceleration does it experience?

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An 800-N billboard worker stands on a 4.0-m scaffold weighing 500 N and supported by vertical ropes at each end.How far would the worker stand from one of the supporting ropes to produce a tension of 770 N in that rope?

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A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape.Each baton was 0.90 m long and each ball on the end is 0.20 kg.(Ignore the mass of the rods. )What is the moment of inertia if the arrangement is spun around an axis formed by one of the batons?

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A 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?

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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 2.50 m rod with a mass of 3.00 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?

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A uniform rod of length L and mass M is pivoted about one end.Attached to the rod is a mass M at its midpoint and at the end opposite the pivot is another mass M.What is the moment of inertia of this configuration about the pivot?

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1300 rev/min is equivalent to which of the following?

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A fan blade,initially at rest,rotates with a constant acceleration of 0.025 rad/s2.What is its angular speed at the instant it goes through an angular displacement of 10 rad?

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Two hoops or rings (I = MR2)are centered,lying on a turntable.The smaller ring has radius = 0.050 m;the larger has radius = 0.10 m.Both have a mass of 6.0 kg.What is the total moment of inertia as the turntable spins? Ignore the mass of the turntable.

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A uniform,horizontal beam of length 6.0 m and weight 140 N is attached at one end to a wall by a pin connection (so that it may rotate).A cable attached to the wall above the pin supports the opposite end.The cable makes an angle of 60° with the horizontal.What is the tension in the cable needed to maintain the beam in equilibrium?

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An object consists of a rod (of length 3.0 m and negligible moment of inertia)to which four small 2.0-kg masses are attached,one at each end and one at each point on the rod 1.0 m from each end.(The masses are one meter apart. )The moment of inertia of this object about an axis perpendicular to the rod and through one of the end masses:

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A 0.30-m radius automobile tire rotates how many rad after starting from rest and accelerating at a constant 3.0 rad/s2 over a 5.0-s interval?

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A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20 s.It is then turned off and coasts to a stop in an additional 60 s.The ratio of the average angular acceleration for the first 20 s to that for the last 60 s is which of the following?

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A 3.0-m rod is pivoted about its left end.A force of 10 N is applied perpendicular to the rod at a distance of 1.2 m from the pivot causing a ccw torque,and a force of 5.2 N is applied at the end of the rod 3.0 m from the pivot.The 5.2-N force is at an angle of 30o to the rod and causes a cw torque.What is the net torque about the pivot? (Take ccw as positive. )

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A ceiling fan is turned on and reaches an angular speed of 60 rev/min in 20 s.It is then turned off and coasts to a stop in 40 s.In the one minute of rotation,through how many revolutions did the fan turn?

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Calculate the linear speed due to the Earth's rotation for a person at a point on its surface located at 30o N latitude.The radius of the Earth is 6.40 × 106 m.

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A 0.20-m radius grinding wheel starts at rest and develops an angular speed of 12.0 rad/s in 4.0 s.What is the average tangential acceleration of a point on the wheel's edge?

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A uniform meterstick balances on a fulcrum placed at the 40-cm mark when a weight W is placed at the 20-cm mark.What is the weight of the meterstick?

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