The text that follow summarize the basic steps toward problem solutions for several problem solving situations. These steps are not intended, nor can they, replace a solid foundation in the basic physical concepts involved. What they can do, is provide the student with a systematic way to start a solution.

I. Kinematics

linear - rotational

1. draw a labeled geometric model (sketch)
2. you need a minimum of 5 labels written like
   • V0 = ? if you do not know the value
   • V0 = (#) m/s if you do know the value
     
3. the five labels are (linear ones on the left, rotational ones on the right;

V0	w0
Vf	wf
x,y,or R	q
a	a
t	t

4. The temporal model-how the problem develops in time

5. Write the "Big Five" equations IF the acceleration is constant

6. Substitute known values from your geometric/temporal model

7. solve your equations for unknowns

II. Dynamics

1. Use the same steps (1-4) in Kinematics
    

2. Draw the interaction diagram

• select the object(s)
• one force for each place the object touches another (can be represented by the x and y components of the force)
  
• gravitational force
• draw all forces as 'pulls' on the object through the center of mass
• include (m ) the coefficient of friction with your labels
• write frictional forces (if any) in the form of f = mN
• 
  

3. Now use same steps 5-7 in Kniematics except

• you have two more equations
  

SF =ma

f = mN

write all force in the form F = F_xi + F_yj + F_zk
where F_x = Fcosq, F_y = Fsinq :   q is measured from the + x-axis !!

III. Energy considerations

1. Start with the models as described in I and II above

2. Write the work-energy equations

3. Solve equations

 

IV. Conservation of Energy

1. Same geometric/temporal models from above (interaction diagrams not necessary)

2. write conservation of energy equations

• DE = 0  expand this equation to;
• D E= D U_g+DU_s+D K
  

ask the questions,

1. is there a change in height?
2. is there a spring?
3. is there a change in speed

note that D = final value - initial value
and;

K = ½M V²
U_g = mgy
U_s = ½kX²

V. Static Equilibrium: when Velocity and acceleration =0

1. geometric model as always

2. interaction diagram

3. SF=0
write all force in the form F = F_xi + F_yj + F_zk

where F_x = Fcosq, F_y = Fsinq :   q is measured from the + x-axis !!

4. Torque : St=0

• select axis of rotation
• for each force F, find the lever arm l_f
• write the equation St=0 with clockwise being negative torque and counter-clockwise being positive torque

5.solve the equations