You are designing a flywheel to store kinetic energy. If all of the following uniform objects have the same mass and same angular velocity , which one will store the greatest amount of kinetic energy? Which will store the least? Explain, (a) A solid sphere of diameter D rotating about a diameter; (b) a solid cylinder of diameter D rotating about an axis perpendicular to each face through its center, (c) a thin-walled hollow cylinder of diameter D rotating about an axis perpendicular to the plane of the circular face at its center; (d) a solid, thin bar of length D rotating about an axis perpendicular to it at its center.
You are designing a flywheel to store kinetic energy. If all of the following uniform objects have the same mass and same angular velocity , which one will store the greatest amount of kinetic energy? Which will store the least? Explain, (a) A solid sphere of diameter D rotating about a diameter; (b) a solid cylinder of diameter D rotating about an axis perpendicular to each face through its center, (c) a thin-walled hollow cylinder of diameter D rotating about an axis perpendicular to the plane of the circular face at its center; (d) a solid, thin bar of length D rotating about an axis perpendicular to it at its center.
You are designing a flywheel to store kinetic energy. If all of the following uniform objects have the same mass and same angular velocity, which one will store the greatest amount of kinetic energy? Which will store the least? Explain, (a) A solid sphere of diameter D rotating about a diameter; (b) a solid cylinder of diameter D rotating about an axis perpendicular to each face through its center, (c) a thin-walled hollow cylinder of diameter D rotating about an axis perpendicular to the plane of the circular face at its center; (d) a solid, thin bar of length D rotating about an axis perpendicular to it at its center.
Definition Definition Rate of change of angular displacement. Angular velocity indicates how fast an object is rotating. It is a vector quantity and has both magnitude and direction. The magnitude of angular velocity is represented by the length of the vector and the direction of angular velocity is represented by the right-hand thumb rule. It is generally represented by ω.
5.48 ⚫ A flat (unbanked) curve on a highway has a radius of 170.0 m.
A car rounds the curve at a speed of 25.0 m/s. (a) What is the minimum
coefficient of static friction that will prevent sliding? (b) Suppose that the
highway is icy and the coefficient of static friction between the tires and
pavement is only one-third of what you found in part (a). What should
be the maximum speed of the car so that it can round the curve safely?
5.77 A block with mass m₁ is placed on an inclined plane with
slope angle a and is connected to a hanging block with mass m₂ by a
cord passing over a small, frictionless pulley (Fig. P5.74). The coef-
ficient of static friction is μs, and the coefficient of kinetic friction is
Mk. (a) Find the value of m₂ for which the block of mass m₁ moves up
the plane at constant speed once it is set in motion. (b) Find the value
of m2 for which the block of mass m₁ moves down the plane at constant
speed once it is set in motion. (c) For what range of values of m₂ will
the blocks remain at rest if they are released from rest?
Chapter 9 Solutions
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