##
angular momentum

Overview page. Subjects: Science and Mathematics.

Symbol *L*. The product of the angular velocity of a body and its moment of inertia about the axis of rotation, i.e. *L* = *I*ω.

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centre of mass

Overview page. Subjects: Mathematics.

The point at which the whole mass of a body may be considered to be concentrated. This is the same as the **centre of gravity**, the point at which the whole weight of a body may be considered...

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compound pendulum

Overview page. Subjects: Mathematics.

A pendulum consisting of a rigid body that is free to swing about a horizontal axis. Suppose that the centre of gravity of the rigid body is a distance *d* from the axis, *m* is the mass of the...

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conservation of angular momentum

Overview page. Subjects: Science and Mathematics — Sports and Exercise Medicine.

The postulate, based on Newton's first law, that a rotating body will continue to turn about its axis of rotation with constant angular momentum unless an extended couple or eccentric force...

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density distribution within the Earth

Overview page. Subjects: Earth Sciences and Geography.

Our estimates of the total mass of the Earth, *M*, and therefore its mean density, rely on the measurement of gravity. Outside the Earth, at a distance *r* from the centre, this is, by Newton's...

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energy of rotation

Overview page. Subjects: Sports and Exercise Medicine.

The kinetic energy associated with rotation of a mass about an axis. It is expressed by *E* = *Iw*
^{2}, where *E* is the kinetic energy of the mass, *I* is the mass's moment of inertia,...

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inertia

Overview page. Subjects: Science and Mathematics.

The tendency of an object to remain at the same velocity, or at rest, unless a force acts on it.

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parallel Axis Theorem

Overview page. Subjects: Sports and Exercise Medicine — Mathematics.

The following theorem about moments of inertia of a rigid body:

Theorem

Let *I*
_{
C
} be the moment of inertia of a rigid body about an...

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Perpendicular Axis Theorem

Overview page. Subjects: Mathematics.

The following theorem about moments of inertia of a lamina:

Theorem

Suppose that a rigid body is in the form of a lamina lying in the plane *z*=0. Let *I*
_{null...}

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phase transitions in the mantle

Overview page. Subjects: Earth Sciences and Geography.

Measurement of the velocity of seismic waves and determination of the Earth's moment of inertia indicate that at depths of 80–100km there appears to be a low velocity zone and from 400–900...

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physical libration

Overview page. Subjects: Astronomy and Astrophysics.

A real periodic variation in the rotation rate of a celestial object, as distinct from an optical libration. In addition to its familiar optical librations, the Moon also possesses a very...

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principle moment of inertia

Overview page. Subjects: Sports and Exercise Medicine.

The moment of inertia of the whole body with respect to one of the principal axes.

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product of inertia

Overview page. Subjects: Mathematics.

A quantity similar to a moment of inertia, but relating to a rigid body and a pair of given perpendicular axes. The products of inertia occur in the inertia matrix which arises in...

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radius of gyration

Overview page. Subjects: Sports and Exercise Medicine — Science and Mathematics.

Symbol *k*. The square root of the ratio of the moment of inertia of a rigid body about an axis to the body's mass, i.e. *k*
^{2} = *I*/*m*, where *I* is the body's moment of inertia and *m* i...

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rotational inertia

Overview page. Subjects: Sports and Exercise Medicine.

A body's resistance to a change in its state of angular motion. It is also called the moment of inertia.

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rotational motion

Overview page. Subjects: Physics.

The laws relating to the rotation of a body about an axis are analogous to those describing linear motion. The **angular displacement** (θ) of a body is the angle in radians through which a...