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Solid Sphere
Often used in problems involving rolling motion.
Hollow Sphere
Useful in problems involving shells or spherical objects like hollow balls.
Solid Cylinder
Important in applications like wheels and axles.
Hollow Cylinder
Relevant in problems involving pipes or cylindrical shells.
Thin Rod (Rotating About Its Center)
Useful in pendulum-like systems.
Thin Rod (Rotating About Its End)
Important in analyzing lever systems.
Rectangular Plate (Rotating About Its Center)
Useful in engineering applications with flat surfaces.
Circular Disk (Rotating About Its Center)
Common in problems involving rotating machinery or flywheels.
Thin Hoop (Rotating About Its Diameter)
Relevant in analyzing rotational dynamics of rings or hoops.
Parallel Axis Theorem
Essential for solving complex rotational problems involving shifting axes.
Parallel Axis Theorem
This theorem allows you to calculate the moment of inertia when the axis of rotation is not the center of mass but is parallel to it.
axis of rotation
When the ______ is shifted from the center of mass, the Parallel Axis Theorem helps adjust the moment of inertia by adding md2md^2md2, where d is the distance between the center of mass and the new axis.
central diameter
Since the mass is all at the outer edge of the thin hoop, its moment of inertia is significant. This concept is applied in systems like rotational disks or wheels that rotate around a ______.
mass
In circular disks, ____ is uniformly distributed along the radius of the disk.
length and width
The formula for a rectangular plate shows how the dimensions of the object (____) influence the moment of inertia. This is important in structural analysis or systems where flat, rectangular plates rotate.
increases
When a thin rod rotates about an end rather than its center, the moment of inertia ______.
axis
The entire length of the rod contributes more to the rotational inertia when farther from the ____, as seen in lever systems or systems involving rods hinged at one end.
Axis
____ around which the object rotates, affecting its resistance to angular acceleration.
solid sphere
Since the mass is concentrated at the outer radius, the hollow sphere has a higher moment of inertia than a ______. This is relevant in analyzing objects that rotate around their center, such as spherical shells or thin-walled spherical objects.
hollow spheres
The solid sphere's moment of inertia is lower than that of ________, reflecting the fact that mass further from the center contributes more to rotational inertia.
Note 
Flashcard (59)