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TOPIC 2: Kinematics and Dynamics

Tip 1:

The 4 main equations in Kinematics are:

v = u + at
s = ut + ½at²
v² = u² + 2as
s = [(u+v)/2] t

These equations should not be used in their raw form, as written above. Instead, you should break them into x and y components, as follows:

                                                 v_x = u_x + a_xt            v_y = u_y + a_yt
                                                s_x = u_xt + ½a_xt² s_y = u_yt + ½a_yt²
                                                v_x² = u_x² + 2a_xs_x   v_y² = u_y² + 2a_ys_y
                                                s_x = [(u_x+v_x)/2] t      s_y = [(u_y+v_y)/2] t

For example, in a projectile problem, where a canon ball is projected at a speed of 20 m s^-1 at an angle of 30º to the horizontal, it would be wrong to just let u = 20 m s^-1 and start calculating. Instead, you should use u_x = 20 cos 30º = 17 m s^-1 and u_y = 20 sin 30º = 10 m s^-1.

Tip 2:

Instead of just writing F = ma, it is better to write it as åF = ma, since it is the resultant force that is equal to mass x acceleration.

The left hand side of the equation contains the resultant of all forces acting on the body. Note that the weight of the body, mg, should be part of these forces (ie. on the left hand side of the equation), and not on the right hand side (a common mistake by students is to replace "ma" with "mg").

Tip 3:

When solving Dynamics problems, always:

1. Draw the free-body-diagram, with all forces acting on the body.

2. Indicate which direction to assign as the positive convention.

3. Indicate the direction of acceleration and label it "a".