MECHANICS

1. Galilean Equations of Motion under Constant Acceleration
                       (No s)
                  (No v)
                 (No t)
   
   where   a = constant acceleration
   u = initial velocity
   v = final velocity
   s = displacement
   and       t = time taken.
   
   Note: For a projectile at maximum height the speed is zero.
2. 
   where p is momentum, m is mass and v is velocity.
3. Conservation of Momentum
   
   where a pair of masses  and  have velocities  and  respectively.
   After they interact they have velocities  and  respectively.
4. or
   where F is force, p is momentum and t is time
   or         F is average force, m is mass, v is final velocity and u is initial velocity.
5. Newton’s Second Law.
   
   where F is force, m is mass and a is acceleration.
6. 
   where W is the weight of an object of mass m and g is the acceleration due to gravity.
7. and
   where x is the horizontal component and y is the vertical component of a vector v which is at angle of  to the horizontal.

8. 
   where P is pressure, F is force and A is area.

9. 
   where  is the density of a body with mass m and volume V.
10. 
    where P is the pressure in a fluid,  is the density of the fluid, g is the acceleration due to gravity and h is the depth at which the pressure is being taken.
11. Boyle’s Law
    
    where P is the pressure of an ideal gas and V is its volume.
12. 
    where F is the gravitational force between a mass  and a mass  separated by a distance of d metres and where G is the universal gravitational constant.
13. 
    where g is the acceleration due to gravity at a distance d from a planet of mass M.
    G is the universal gravitational constant.
14. 
    where M is the moment of a force F applied at a distance d from a given point.
15. 
    where T is the torque (moment) of a couple, i.e. a pair of force each of magnitude F, having opposing directions and separated by a distance d.
16. 
    where W is the work done when a force F moves a body a distance s in the direction of the force.
17. 
    where  is the kinetic energy of a body of mass m and velocity v.
18. 
    where  is the potential energy required to move a mass m a vertical distance h and g is the acceleration due to gravity.
19. 
    where P is the average power when W is the work done in a time t.
20. 
21. 
    where  is the angle in radians corresponding to an arc length l in a circle of radius length r.
22. 
    where  is the average angular speed when a body in circular motion traces an angle of  radians in t seconds.
23. 
    where v is the tangential velocity of an object moving in a circle of radius length r with a constant angular speed .
24.            or        
    where a is the centripetal acceleration of a body moving in a circle of radius length r with a constant angular velocity  and a tangential velocity v.
25. or
    where F is the centripetal force required to keep a body of mass m moving in a circle of radius r. The body moves with a constant angular velocity  and a tangential velocity v.
26. 
    where v is the speed of a satellite in a circular orbit of radius R around a planet of mass M. G is the universal constant of gravitation.
27. 
    where T is the period of a satellite moving at a constant velocity v in a circular orbit of radius R.
28. Kepler’s Third Law
    
    where T is the period of a a circular orbit of radius R around a planet of mass M.  G is the universal constant of gravitation.
29. 
    where R is the radius of a circular orbit of period T around a planet of mass M.  G is the universal constant of gravitation.
    
    Note: for a geostationary or parking orbit T = one day = 86, 400 seconds. The height, h, of such an orbit is given by , where r is the radius of the planet..
30. Hooke’s Law
    
    where F is the force required to give a spring a displacement s and k is a constant of proportionality. (Note: the spring must not be extended by beyond its elastic limit.)
31. 
    where a is the acceleration of a body moving in simple harmonic motion when it has a displacement s from its equilibrium position. The constant of proportionality is given by .
32. 
    where T is the period of a body moving in simple harmonic motion with a constant of proportionality .
33. 
    where T is the period of a simple pendulum of length l and g is the acceleration due to gravity.