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Chapter 10: Q89P (page 293)
A bicyclist of mass puts all his mass on each downward moving pedal as he pedals up a steep road. Take the diameter of the circle in which the pedals rotate to be , and determine the magnitude of the maximum torque he exerts about the rotation axis of the pedals.
Magnitude of maximum torque is
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Two uniform solid cylinders, each rotating about its central (longitudinal) axis at 235rad/s, have the same mass of 1.25kg but differ in radius. What is the rotational kinetic energy of (a) the smaller cylinder, of radius 0.25m, and (b) the larger cylinder, of radius 0.75m?
Our Sun is (light-years) from the center of our Milky Way galaxy and is moving in a circle around that center at a speed of . (a) How long does it take the Sun to make one revolution about the galactic center? (b) How many revolutions has the Sun completed since it was formed about years ago?
A high-wire walker always attempts to keep his center of mass over the wire (or rope). He normally carries a long, heavy pole to help: If he leans, say, to his right (his com moves to the right) and is in danger of rotating around the wire, he moves the pole to his left (its com moves to the left) to slow the rotation and allow himself time to adjust his balance. Assume that the walker has a mass of and a rotational inertia of about the wire.What is the magnitude of his angular acceleration about the wire if his com is to the right of the wire and (a) he carries no pole and (b) the pole he carries has its com 10 cm to the left of the wire?
Attached to each end of a thin steel rod of length and mass is a small ball of mass . The rod is constrained to rotate in a horizontal plane about a vertical axis through its midpoint. At a certain instant, it is rotating at . Because of friction, it slows to a stop in .Assuming a constant retarding torque due to friction, compute
(a) the angular acceleration,
(b) the retarding torque,
(c) the total energy transferred from mechanical energy to thermal energy by friction, and
(d) the number of revolutions rotated during the .
(e) Now suppose that the retarding torque is known not to be constant. If any of the quantities (a), (b), (c), and (d) can still be computed without additional information, give its value.
The rigid object shown in Fig.consists of three ballsand three connecting rods, withand. The balls may be treated as particles, and the connecting rods have negligible mass. Determine the rotational kinetic energy of the object if it has an angular speed ofabout (a) an axis that passes through point P and is perpendicular to the plane of the figure and (b) an axis that passes through point P, is perpendicular to the rod of length, and lies in the plane of the figure.
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