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Exam 8: Rotational Motion

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Question 1

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A Ferris wheel, rotating initially at an angular speed of 0.16 rad/s, accelerates over a 7.0-s interval at a rate of 0.050 rad/s². What is its angular speed after this 7.0-s interval?

A) 0.46 rad/s
B) 0.85 rad/s
C) 0.51 rad/s
D) 1.2 rad/s

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Question 2

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A Ferris wheel starts at rest and builds up to a final angular speed of 0.70 rad/s while rotating through an angular displacement of 2.5 rad. What is its average angular acceleration?

A) 0.098 rad/s²
B) 0.05 rad/s²
C) 1.8 rad/s²
D) 0.60 rad/s²

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Question 3

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Suppose a car has a 100,000 mile 10 year warranty on the wheels and axles of a car. How may turns will the wheels of 0.80-m diameter make if both the mileage and time warranties run out simultaneously and what will be the average angular velocities of the wheel? Assume that a mile = m and that a year is s.

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?

A bowling ball has a mass of 7.0 kg, a moment of inertia of 2.8 * 10^-2 kg·m², and a radius of 0.10 m. If it rolls down the lane without slipping at a linear speed of 5.0 m/s, what is its angular speed?

A meterstick is supported by a knife-edge at the 50-cm mark. Doug hangs masses of 0.40 and 0.60 kg from the 35-cm and 80-cm marks, respectively. Where should Doug hang a third mass of 0.30 kg to keep the stick balanced?

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?

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 30^o to the rod and causes a cw torque. What is the net torque about the pivot? (Take ccw as positive.)

Two children seat themselves on a seesaw. The one on the left has a weight of 400 N while the one on the right weighs 300 N. The fulcrum is at the midpoint of the seesaw. If the child on the right is not at the end but is 1.50 m from the fulcrum and the seesaw is balanced, what is the torque provided by the weight of the child on the left? (Take ccw as positive.)

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 x axis?

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?

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?

A 0.200-kg object is swung in a circular path and in a vertical plane on a 0.500-m length string. If the angular speed at the bottom is 8.00 rad/s, what is the tension in the string when the object is at the bottom of the circle?

Two equal magnitude forces are in opposite directions, and their lines of action are separated by distance d. These two forces are applied to a solid disk, which is mounted on a frictionless axle. If d is half the radius r of the disk, which of the following positions for the forces would give the most torque?

A disk has a moment of inertia of 3.0 *10^-4 kg·m² and rotates with an angular speed of 3.5 rad/sec. What net torque must be applied to bring it to rest within 3.7 s?

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?

The quantity "moment of inertia" (in terms of the fundamental quantities of mass, length, and time) is equivalent to:

A 4.0-kg mass is placed at (3.0, 4.0) m, and a 7.0 kg-mass is placed at (3.0, -.0) m. What is the moment of inertia of this system of masses about the z axis?

A baseball pitcher, loosening up his arm before a game, tosses a 0.15-kg ball using only the rotation of his forearm, 0.32 m in length, to accelerate the ball. If the ball starts at rest and is released with a speed of 24 m/s in a time of 0.40 s, what is the average angular acceleration of the arm and ball?

A non-uniform rod of length L and mass M is pivoted about one end. The moment of inertia of this rod about its pivoted end is . Attached to the rod is a mass M at its midpoint and at the end opposite the pivot is another mass 2M. What is the moment of inertia of this configuration about the pivot?