Physics 1 Review prepared by D Mitrovich 20 July 10 revised 3 June 11 Units review basic length and mass modifiers kilo 1000 centi 1 100 milli 1 1000 review units for mass m length l time t velocity l t acceleration l t2 force Newton N ml t2 weight ml t2 momentum ml t energy Joule J ml2 t2 angular momentum ml2 t torque N m ml2 t2 moment of inertia I ml2 Always include units in your final answer Vectors Physical quantities that have a direction as well as a magnitude are called vec tors shown either in bold type or with a bar over the symbol e g position xor x velocity vor v acceleration aor a If a vector V has components IVx Vy VzM all perpendicular to each other and V W IVx Vy VzM IWx Wy WzM IVx Wx Vy Wy Vz WzM similarly for vector W the vectors can be added subtracted by adding subtrac ting the corresponding components 2 Phys I revu nb If a vector is multiplied by a number all its components are multiplied by the same number cV IcVx cVy cVzM So in particular V I Vx Vy VzM The magnitude of a vector whose components are IVx Vy VzM is V Vx 2 Vy 2 Vz 2 In two dimensions if the two components have the same length Vx Vy the length of the actual vector is 2 Vx Another often seen combination is components in the ratio 3 4 if the components actually have lengths 3 and 4 the length of the vector itself is 5 check it using the above expression A change in some quantity X say from X1 to X2 is usually denoted by DX X2 X1 So v Dx Dt x2 x1 t2 t1 and a Dv Dt v2 v1 t2 t1 and the quantity x1 corresponds to t1 etc Motion diagrams Mark an object s changing positions by taking snapshots of its positions at equal time intervals The object s velocity vector at any one of these marks can be shown as an arrow pointing from that mark to the next one the velocity vector is always tangent to the trajectory curve Phys I revu nb 3 Review basic trigonometry sin b b c cos b a c tan b b a c a b b 90o In a 2 dimensional right angle coordinate system reference frame to be chosen first such as Hx yL a vector s components Ivx vyM can be expressed in vx v cosHbL and vx v sinHbL terms of its magnitude v vx2 vy2 as where b is the angle from the x axis to the vector itself If two vectors v1 and v2 are given in terms of their magnitudes and angles in stead of their components you can add them by converting both to components using the above expressions and then adding those You can convert the final vector back to magnitude and new angle g by using g sin 1J vy vN cos 1J vx vN tan 1J vy vx N Graphically you can show the result of adding two vectors by either of two ways 1 parallelogram method put the tails of the two vectors at the same point and let the two vectors define a parallelogram the opposite point is the head of the resulting vector shown dashed B A A B A B A B 4 Phys I revu nb 2 stacking method keeping it always pointing in the same direction slide one vector until its tail is at the head of the other one the position of its head of the vector you slid is also the position of the head of the resulting vector B A A B A A B B Kinematics If an object s velocity vector v is constant during a time interval Dt its change in position during that time is D x v Dt if v is constant If the object is accelerating at a constant rate a during time interval Dt the changes in its velocity and position during that time are D v a Dt and D x v 0 Dt 1 where v 0 is the velocity at the start of the interval Note that the last term can also be written as 2 a Dt2 1 1 2 2 a Dt2 if a is constant ID vM2 Dt Note also that the signs or directions of v and a as well as their magni tudes are independent of each other Newton s 2nd law F ma Finertial ma A net force F exerted on a mass m will cause that mass to accelerate according to the relation The mass m being accelerated will react by pushing back with the inertial force so that the total force in the system F Finertial is zero Phys I revu nb 5 If the y axis is positive upwards the force of gravity on a mass m its weight at sea level is Fy mg where g 9 8 m s2 If that mass is in free fall its acceleration is ay g remember to keep track of the sign of g If two masses m and M are attached to each other so their speeds and accele rations are the same but mass m moves vertically and so feels the force of gravity while mass M moves horizontally and does not the force exerted on this system is F mg and the inertial force from the common acceleration a is Finertial Im MM a Since the sum of these forces is zero the acceleration is given by mIm MM g a If the mass is on an incline the gravitational force on it can be split into components parallel with and perpendicular to the incline The perpendicu lar part is opposed by the normal force FN from the incline surface and the parallel part is opposed by the friction force Ff and the inertial force Finertial Newton s 3rd law This law simply says that in a static non moving system for every force F there is an equal and opposite reaction force Freaction such that F Freaction 0 Finertial Freaction By defining the inertial force as we did above Finertial m a Newton s 3rd law can be generalized to a dynamic moving system by setting 6 Phys I revu nb F 0 In this case for every collection of masses and forces we can write with inertial forces being included in the sum Some general types of forces are FI inertial Fg gravitational FT tension from string rope chain FN normal perpendicular to surface Ff parallel to surface e g friction Work energy In an isolated system energy is conserved There are many kinds of energy including kinetic chemical potential nuclear gravitational electromagnetic thermal etc energyD AforceE xAlengthE ml2 t2 Energy is a scalar quantity no direction Its units are In SI metric units this is Newton meters N l also called the Joule abbreviated J Work is just the transfer of mechanical energy by moving some distance in parallel with an applied force Any motion perpendicular to a force involves …