Name: rigid body motion: forces and moments
Uploaded: 2024-03-07T13:22:25.000Z
Duration: 1 min 22 s
Channel: JoVE

The motion of a rigid body in a general plane occurs due to externally applied forces and couple moments acting upon it.
Newton&#39;s second law gives the translational motion of the center of mass of the body along each axis.
Furthermore, the rotation of the body&#39;s center of mass caused by couple moments can be expressed as the product of the moment of inertia and the angular acceleration.
These equations of motion can be generalized to any point on the body by expressing the moment equation as the sum of the moment about the center of mass and the moment due to translational motion about that specific point.
For the object undergoing rolling without slipping, the moment equation for the point O is the sum of the moment due to the center of mass and the moment due to the translational motion of the center of mass.
In this case, using a parallel axis theorem, the moment equation can be expressed in terms of the moment of inertia of the object at about point O.

equation of motion: general plane motion

Equation of Motion: General Plane motion

In the context of a rigid body&#39;s movement within a general plane, it is important to understand that this motion is typically triggered by external forces or couple moments exerted onto it. This principle can be explained through Newton&#39;s second law, which stipulates the translational motion of the body&#39;s center of mass along each axis.
Moreover, the body&#39;s center of mass experiences a rotational effect as a result of these couple moments. This rotation can be articulated as the product of the angular acceleration and the moment of inertia. These equations of motion can be extended to any point on the body. This can be achieved by representing the moment equation as the sum of two components: the moment about the center of mass and the moment due to the translational motion about a specific point on the body.
For an object that rolls without slipping, there is a specific moment equation for the point in contact with the floor, point O. This equation is the summation of the moment due to the translational motion of the center of mass and the moment due to the center of mass itself. In such instances, the moment equation can be expressed using the parallel axis theorem. This theorem allows us to represent the moment equation in terms of the moment of inertia of the object at about point O. The exploration of these principles provides valuable insights into the intricate dynamics of a rigid body&#39;s motion within a general plane.

The motion of a rigid body in a general plane occurs due to externally applied forces and couple moments acting upon it.
Newton&#39;s second law gives the ...

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JoVE Core

Mechanical Engineering

Unit 1

Planar Kinematics of a Rigid Body

KEY TERMS AND CONCEPTS

rigid body motion: forces and moments

Rigid body motion in a general plane is driven by external forces and couple moments. The body moves and turns at the same time. Newton’s second law describes the translational motion of the center of mass along each axis.

The center of mass also rotates because of the applied couple moments. That rotation is described by angular acceleration and moment of inertia. These two quantities connect the turning effect to how hard the body is to rotate.

The same motion equations can be written for any point on the body. To do this, the moment equation is split into two parts. One part is the moment about the center of mass, and the other is the moment from the translational motion about a chosen point.

For an object that rolls without slipping, the point in contact with the floor is often called point O. A special moment equation can be written for that point. It combines the moment from the center of mass motion and the moment about the center of mass itself.

In this case, the parallel axis theorem is useful. It lets the moment equation be written using the moment of inertia about point O. This gives a clear way to study rigid body motion in a general plane.

Rigid Body Motion: Forces and Moments

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Rigid body motion in a general plane is driven by external forces and couple moments. The body moves and turns at the same time. Newton’s second law describes the translational motion of the center of mass along each axis. The center of mass also rotates because of the applied couple moments. That rotation is described by angular acceleration and moment of inertia. These two quantities connect the turning effect to how hard the body is to rotate. The same motion equations can be written for...

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key terms and concepts

Explore how external forces and couple moments drive rigid body motion, including center of mass translation, rotation, and rolling without slipping.

Rigid Body Motion: Forces and Moments | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

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Rigid Body Motion: Forces and Moments

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