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Kinematic Equations for Rotation

Kinematic Equations for Rotation

In mechanics, when one observes a rigid body in rotational motion with constant angular acceleration, it is possible to establish equations for its rotational kinematics. This process resembles how linear kinematics are dealt with in simpler motion studies.
For instance, imagine a point A on a rigid body engaged in circular motion. The translational velocity of this particular point can be calculated by taking the time derivatives of the displacement equation, which essentially measures the...

Kinematic Equations - II

Kinematic Equations - II

The second kinematic equation expresses the final position of an object in terms of its initial position, the distance traveled with the initial constant velocity, and the distance traveled due to a change in velocity. Similar to the first kinematic equation, this equation is also only valid when the acceleration is constant throughout the motion of an object.
Suppose a car merges into freeway traffic on a 200 m long ramp. If its initial velocity is 10 m/s and it accelerates at 2 m/s2, then the...

Kinematic Equations - III

Kinematic Equations - III

The first two kinematic equations have time as a variable, but the third kinematic equation is independent of time. This equation expresses final velocity as a function of the acceleration and distance over which it acts. The fourth kinematic equation does not have an acceleration term and provides the final position of the object at time t in terms of the initial and final velocities. This equation is useful when the value of the constant acceleration is unknown.
Using the kinematic equations,...

Kinematic Equations - I

Kinematic Equations - I

When an object moves with constant acceleration, the velocity of the object changes at a constant rate throughout the motion. The kinematic equations of motions are derived for such cases where the acceleration of the object is constant. The first kinematic equation gives an insight into the relationship between velocity, acceleration, and time. We can see, for example:

Kinematic Equations: Problem Solving

Kinematic Equations: Problem Solving

When analyzing one-dimensional motion with constant acceleration, the problem-solving strategy involves identifying the known quantities and choosing the appropriate kinematic equations to solve for the unknowns. Either one or two kinematic equations are needed to solve for the unknowns, depending on the known and unknown quantities. Generally, the number of equations required is the same as the number of unknown quantities in the given example. Two-body pursuit problems always require two...

Relative Motion Analysis - Acceleration

Relative Motion Analysis - Acceleration

A slider-crank mechanism converts rotational motion from the crank into linear motion of the slider or vice versa. This mechanism consists of three main parts: the crank, the connecting rod, and the slider. The movement of the slider-crank is an example of general plane motion as the fluctuating angle between the crank and the connecting rod. Consider a segment AB where point A is at the end of the slider and point B is on the diametrically opposite end to point A, on a crack. The variance in...

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Related Experiment Video

Updated: Jun 12, 2026

Sit-to-stand-and-walk from 120% Knee Height: A Novel Approach to Assess Dynamic Postural Control Independent of Lead-limb

Sit-to-stand-and-walk from 120% Knee Height: A Novel Approach to Assess Dynamic Postural Control Independent of Lead-limb

Published on: August 30, 2016

Effect of registration on cyclical kinematic data.

Elizabeth A Crane¹, Ruth B Cassidy, Edward D Rothman

¹Department of Biologic and Materials Sciences, School of Dentistry, University of Michigan, Ann Arbor, MI 48109-1078, USA. bcrane@umich.edu

Journal of Biomechanics

|June 12, 2010

Summary

Registration may not always be necessary for analyzing human movement data, especially cyclical chewing data. This study presents methods to assess if registration improves biomechanical analyses using functional data analysis (FDA).

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Four-Dimensional CT Analysis Using Sequential 3D-3D Registration

Four-Dimensional CT Analysis Using Sequential 3D-3D Registration

Published on: November 23, 2019

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Last Updated: Jun 12, 2026

Sit-to-stand-and-walk from 120% Knee Height: A Novel Approach to Assess Dynamic Postural Control Independent of Lead-limb

Sit-to-stand-and-walk from 120% Knee Height: A Novel Approach to Assess Dynamic Postural Control Independent of Lead-limb

Published on: August 30, 2016

Four-Dimensional CT Analysis Using Sequential 3D-3D Registration

Four-Dimensional CT Analysis Using Sequential 3D-3D Registration

Published on: November 23, 2019

Area of Science:

Biomechanics
Functional Data Analysis (FDA)
Human Movement Analysis

Background:

Functional data analysis (FDA) is increasingly used for human movement.
Registration is a standard FDA procedure to reduce phase variability in cyclical data.
Understanding registration's impact on biomechanical analysis is crucial.

Purpose of the Study:

Assess the necessity of registration for time-normalized cyclical data.
Illustrate three methods for evaluating the effects of registration on biomechanical data.

Main Methods:

Analyzed masticatory jaw movements from 22 healthy adults.
Captured motion data at 60 Hz using video cameras.
Applied time normalization and functional data transformation to chewing cycles.

Main Results:

Registration did not significantly alter mean curves or linear warping functions.
Registration slightly decreased root-mean-square (RMS) values, indicating reduced variability, but not significantly.
The necessity of registration for cyclical chewing data was questioned.

Conclusions:

Registration may not be essential for all cyclical biomechanical data, such as chewing.
Three practical methods for evaluating registration effects were demonstrated.
These methods aid in determining if additional data manipulation is required.