Euler’s First Law (continued)

Key Concept: The starting point for all applications in kinetics is to construct a complete and

accurate free body diagram detailing all external forces and all external moments. The free

body diagram should also include all dimensions, angles, and frame of reference with the

assumed positive directions.

Strategy:

Step 1: Identify all external forces acting on the particle (rigid body) by

constructing a free body diagram.

Step 2: Apply Euler’s first law (equations of motion). In plane motion, there are two scalar equations

of motion governing the motion of its center of mass. In vector form this law is:

ΣF = m a = m dv/dt = m a_c (vector equation)

In scalar form the equations of motion in x-y plane are:

Rectangular coordinates	Σ Fx = max	Σ Fy = may
Polar coordinates	Σ Fr = mar	Σ Fθ = maθ
Intrinsic coordinates	Σ Ft = mat	Σ Fn = man

Step 3: Check to see the number of unknowns in the scalar equations of motion equal

the number of equations. These unknowns typically include forces and accelerations.

Frequently there are more unknowns than scalar equations. So you will need to

supplement the scalar equations of motion with other relations.

Forms of Additional Information include:

For velocity or displacement you will need to integrate the equations of motion

Sliding or impending sliding involves friction. You will then need to relate the
friction force to the normal force by F = μ N

For rolling you will need to use kinematics to relate the translational acceleration
to the rotational acceleration or the translational velocity to the angular velocity.

Click here to go to discussion of Euler’s second Law.

Click here for examples.

Return to Notes on Dynamics

Copyright © 2019 Richard C. Coddington
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