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Symbolic Solutions (and General Strategy)

Key Concept: Values of forces (F), moments (M), dimensions such as lengths (L) and

angles (θ) as well as other terms such as linear velocity (L/T), angular velocity (1/T), linear

acceleration (L/T²), and angular acceleration (1/T²)) are typically provided as input information .

You are then asked to find some result such as an unknown force forces or accelerations.

A preferred approach is to use symbols rather than their values as you step through your
solution. This approach has two distinct benefits.

Benefits of using Symbolic Solutions

Benefit 1

As you proceed through your solution you can check the

dimensions of each term to verify that at each stage of the

solution your results check dimensionally. If they do, then

your calculations are possibly correct. If not, then you have

an error somewhere and you should review the steps leading

up to your result.

Benefit 2

When you arrive at your final result you can investigate the influence

of each variable or parameter on the unknown being calculated.

Also for on-line, assigned problems, the values of input variables

may change. So your symbolic solution will be valid for any set of input data. You can simply enter the latest set of input data to arrive

at your answer.

General Strategy to Solve Dynamics Problems in a Plane

Draw a FBD of one or more parts to identify the forces (and possibly moments)
that act on each part. This is the key step. If incorrect, then all remaining
calculations will be for naught.

Write equations of motion for each part. i.e. ∑ F = ma, ∑ M_C= I_C α

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