The assembly shown in the figure below consists of a thin rod of length = 22.0 cm and mass m - 1.20 kg with a solid sphere of diameter d - 10.0 cm and mass M - 2.00 kg attached to its top. The assembly is free to pivot about a frictionless axle through the bottom of the rod. The assembly is initially vertical and at rest when it starts to rotate clockwise. f @ (a) After the combination rotates through 90 degrees, what is its rotational kinetic energy (in 3)? x How can you apply conservation of energy to the system of the assembly and Earth? What types of energy are changing? What are the positions of the centers of mass of the rod and the sphere? What is the change in height of each? J (b) What is the angular speed (in rad/s) of the rod and sphere? |x How is the rotational kinetic energy of the system related to its angular speed and moment of inertia? How can you find the total moment of inertia of the rod and sphere? What does the parallel-axis theorem say? rad/s (c) What is the linear speed (in m/s) of the center of mass of the sphere? x How is angular speed related to linear speed? What is the distance from the pivot to the center of mass of the sphere? m/s (d) How does it compare with the speed had the sphere fallen freely through the same distance of 27.0 cm? (Express your answer as a percentage of fall.) Vswing is less than X Vall by x What constant acceleration kinematics formula relates the final speed of a falling object to the acceleration and distance fallen? By what percentage of Vfall does Vswing differ from Vall? %.
The assembly shown in the figure below consists of a thin rod of length = 22.0 cm and mass m - 1.20 kg with a solid sphere of diameter d - 10.0 cm and mass M - 2.00 kg attached to its top. The assembly is free to pivot about a frictionless axle through the bottom of the rod. The assembly is initially vertical and at rest when it starts to rotate clockwise. f @ (a) After the combination rotates through 90 degrees, what is its rotational kinetic energy (in 3)? x How can you apply conservation of energy to the system of the assembly and Earth? What types of energy are changing? What are the positions of the centers of mass of the rod and the sphere? What is the change in height of each? J (b) What is the angular speed (in rad/s) of the rod and sphere? |x How is the rotational kinetic energy of the system related to its angular speed and moment of inertia? How can you find the total moment of inertia of the rod and sphere? What does the parallel-axis theorem say? rad/s (c) What is the linear speed (in m/s) of the center of mass of the sphere? x How is angular speed related to linear speed? What is the distance from the pivot to the center of mass of the sphere? m/s (d) How does it compare with the speed had the sphere fallen freely through the same distance of 27.0 cm? (Express your answer as a percentage of fall.) Vswing is less than X Vall by x What constant acceleration kinematics formula relates the final speed of a falling object to the acceleration and distance fallen? By what percentage of Vfall does Vswing differ from Vall? %.
University Physics Volume 1
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Chapter10: Fixed-axis Rotation
Section: Chapter Questions
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Transcribed Image Text:The assembly shown in the figure below consists of a thin rod of length = 22.0 cm and mass m - 1.20 kg with a solid sphere of diameter d - 10.0 cm and mass M - 2.00 kg attached to its top. The assembly is free to pivot about a
frictionless axle through the bottom of the rod. The assembly is initially vertical and at rest when it starts to rotate clockwise.
f
@
(a) After the combination rotates through 90 degrees, what is its rotational kinetic energy (in 3)?
x
How can you apply conservation of energy to the system of the assembly and Earth? What types of energy are changing? What are the positions of the centers of mass of the rod and the sphere? What is the change in height of
each? J
(b) What is the angular speed (in rad/s) of the rod and sphere?
|x
How is the rotational kinetic energy of the system related to its angular speed and moment of inertia? How can you find the total moment of inertia of the rod and sphere? What does the parallel-axis theorem say? rad/s
(c) What is the linear speed (in m/s) of the center of mass of the sphere?
x
How is angular speed related to linear speed? What is the distance from the pivot to the center of mass of the sphere? m/s
(d) How does it compare with the speed had the sphere fallen freely through the same distance of 27.0 cm? (Express your answer as a percentage of fall.)
Vswing is less than X Vall by
What constant acceleration kinematics formula relates the final speed of a falling object to the acceleration and distance fallen? By what percentage of Vfall does Vswing differ from Vall? %.
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