Engr Help

Kinetics – General strategy to solve problems in Kinetics for Plane Motion

In a Nut Shell: In kinetics you analyze the forces and moments acting on a body and the

resultant motion of the body. This resultant motion (acceleration) may include both translation

and rotation. Strategy:

Step 1

Construct a complete and accurate free body diagram of all forces and couples acting

on the body. Include the axes showing + x, +y, and + rotation. Proper signs for acceleration are very important. Step 1 is critical. Without it solution is impossible.

Step 2

Write down the equations of motion for both translation and rotation.

Euler’s 1^st law governs translational motion of the center of mass for a body.

F = m a_c = m dv_c/dt = ma_c

Euler’s 2^nd law governs rotational motion of the body.

M_C = I_C α

If the body only translates (no rotational acceleration), then

M_C = 0

Step 3

Check the total number of unknowns. Most likely you will need additional
information to obtain the solution.

Step 4

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.

Step 5

Verify that the total number of unknowns equals the total number of equations.

Step 6

Solve for the desired unknowns.

Click here for an example.

Return to Notes on Dynamics