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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 30^{o} N latitude. The radius of the Earth is 6.40 10^{6} m.

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C

Which of the first units given below can be units for angular acceleration while the second units can be units for angular velocity?

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C

A bank vault is opened by applying a force of 300 N perpendicular to the plane of the door, 1.2 m from the hinges. Find the torque due to this force about an axis through the hinges.

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D

What is the angular speed about the rotational axis of the Earth for a person standing on the surface?

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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?

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A 0.60-kg rock is swung in a circular path and in a vertical plane on a 0.25-m length string. At the top of the path, the angular speed is 12.0 rad/s. What is the tension in the string at that point?

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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?

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

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Calculate the linear speed due to the Earth's rotation for a person at the equator of the Earth. The radius of the Earth is 6.40 10^{6} m.

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Consider a point on a bicycle wheel as the wheel turns about a fixed axis, neither speeding up nor slowing down. Compare the linear and angular accelerations of the point.

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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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The torque caused by a force F applied at a distance r from the axis of rotation, is given by , where is the angle between and . If the magnitudes r and F remain the same, what other angle will produce the same torque as was produced at angle if was less than 90°?

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A circular disk is rotating about a central axis with an angular velocity which is increasing at a constant rate. Point 1 on the disk is located at a distance from the center of the disk and point 2 on the disk is located at a distance from the center of the disk. If , which of the following ratios is the largest? 1 and 2 refer to being at points 1 and 2 in the subscripts below, all values occurring at the same time.

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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.

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Consider a point on a bicycle wheel as the wheel turns about a fixed axis, neither speeding up nor slowing down. Compare the linear and angular velocities of the point.

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Consider a point on a bicycle wheel as the wheel makes exactly four complete revolutions about a fixed axis. Compare the linear and angular displacements of the point.

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A grindstone spinning at the rate of 12 rev/s has what approximate angular speed?

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Two points on a merry-go-round are located at distances from the center r_{1} and r_{2}, where r_{1} < r_{2}. While the merry-go-round is in the process of speeding up to operational speed, which of the following equations involving magnitudes of angular speed, angular acceleration, and linear speed for these points is incorrect?

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A spool of thread has an average radius of 1.00 cm. If the spool contains 126 m of thread, how many turns of thread are on the spool? "Average radius" allows us to not need to treat the layering of threads on lower layers.

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A 0.12-m radius grinding wheel takes 2.1 s to speed up from 2.0 rad/s to 11.0 rad/s. What is the wheel's average angular acceleration?

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