Part 1: Moment of inertia (Theory) Newton's Second Law states that a torque T applied to a rotating body creates an angular acceleration a in that body given by: a=t/I (Eq 3) where I is a property of the body called the moment of inertia. The moment of inertia is the measure of inertia of the rotating body. It is therefore analogous to mass from linear motion. The moment of inertia of a body about a given axis depends on: (1) the mass of the body (mass increases moment of inertia). (2) the distribution of this mass (the further the mass is distributed from the axis, the higher the body's moment of inertia). Disc Axis Ring Tray Angular acceleration Base M Platform String Figure 1- Basic setup (model) Question 1: The two objects above are each free to rotate about an axis through its centre, as shown. If the two objects have equal mass and the same outer radius, which will have the higher moment of inertia about this axis? Why?
Part 1: Moment of inertia (Theory) Newton's Second Law states that a torque T applied to a rotating body creates an angular acceleration a in that body given by: a=t/I (Eq 3) where I is a property of the body called the moment of inertia. The moment of inertia is the measure of inertia of the rotating body. It is therefore analogous to mass from linear motion. The moment of inertia of a body about a given axis depends on: (1) the mass of the body (mass increases moment of inertia). (2) the distribution of this mass (the further the mass is distributed from the axis, the higher the body's moment of inertia). Disc Axis Ring Tray Angular acceleration Base M Platform String Figure 1- Basic setup (model) Question 1: The two objects above are each free to rotate about an axis through its centre, as shown. If the two objects have equal mass and the same outer radius, which will have the higher moment of inertia about this axis? Why?
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![Part 1: Moment of inertia (Theory)
Newton's Second Law states that a torque T applied to a rotating
body creates an angular acceleration a in that body given by:
a=t/I (Eq 3)
where I is a property of the body called the moment of inertia.
The moment of inertia is the measure of inertia of the rotating
body. It is therefore analogous to mass from linear motion.
The moment of inertia of a body about a given axis depends on:
(1) the mass of the body (mass increases moment of inertia).
(2) the distribution of this mass (the further the mass is
distributed from the axis, the higher the body's moment of
inertia).
Disc
Axis
Ring
Tray
Platform
Angular
acceleration
Base
String
Figure 1- Basic setup (model)
Question 1: The two objects above are each free to rotate about an axis through its centre,
as shown. If the two objects have equal mass and the same outer radius, which will have the
higher moment of inertia about this axis? Why?
Question 2: If the same torque was applied to each of these objects, which object will have
the higher angular acceleration? Why?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7634a6a-5ecc-40e2-9892-46ba7a4cefd4%2F027c9997-7ac3-4b85-aab8-af1308fe8c34%2F80vtkub_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Part 1: Moment of inertia (Theory)
Newton's Second Law states that a torque T applied to a rotating
body creates an angular acceleration a in that body given by:
a=t/I (Eq 3)
where I is a property of the body called the moment of inertia.
The moment of inertia is the measure of inertia of the rotating
body. It is therefore analogous to mass from linear motion.
The moment of inertia of a body about a given axis depends on:
(1) the mass of the body (mass increases moment of inertia).
(2) the distribution of this mass (the further the mass is
distributed from the axis, the higher the body's moment of
inertia).
Disc
Axis
Ring
Tray
Platform
Angular
acceleration
Base
String
Figure 1- Basic setup (model)
Question 1: The two objects above are each free to rotate about an axis through its centre,
as shown. If the two objects have equal mass and the same outer radius, which will have the
higher moment of inertia about this axis? Why?
Question 2: If the same torque was applied to each of these objects, which object will have
the higher angular acceleration? Why?
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