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Chris Parkes

EE1 Particle Kinematics : Newton’s Legacy "If I see further, it is because I stand on the shoulders of giants,". Motion Forces Energy & Momentum Conservation Circular Motion Gravity. Chris Parkes. http://ppewww.ph.gla.ac.uk/~parkes/teaching/PK/PK.html. October 2005. Motion. x. e.g.

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Chris Parkes

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  1. EE1 Particle Kinematics : Newton’s Legacy"If I see further, it is because I stand on the shoulders of giants," Motion Forces Energy & Momentum Conservation Circular Motion Gravity Chris Parkes http://ppewww.ph.gla.ac.uk/~parkes/teaching/PK/PK.html October 2005

  2. Motion x e.g dx • Position [m] • Velocity [ms-1] • Rate of change of position • Acceleration [ms-2] • Rate of change of velocity 0 t dt v 0 t a 0

  3. Equations of motion in 1D • Initially (t=0) at x0 • Initial velocity u, • acceleration a, s=ut+1/2 at2, where s is displacement from initial position v=u+at Differentiate w.r.t. time: v2=u2+2 as

  4. 2D motion: vector quantities Scalar: 1 number Vector: magnitude & direction, >1 number • Position is a vector • r, (x,y) or (r,  ) • Cartesian or cylindrical polar co-ordinates • For 3D would specify z also • Right angle triangle x=r cos , y=r sin  r2=x2+y2, tan  = y/x Y r y  x 0 X

  5. vector addition y b • c=a+b cx= ax +bx cy= ay +by a c can use unit vectors i,j i vector length 1 in x direction j vector length 1 in y direction x scalar product a  finding the angle between two vectors b a,b, lengths of a,b Result is a scalar

  6. Velocity and acceleration vectors Y • Position changes with time • Rate of change of r is velocity • How much is the change in a very small amount of time t r(t) r(t+t) Limit at t0 x 0 X

  7. We described the motion, position, velocity, acceleration, now look at the underlying causes Newton’s laws • First Law • A body continues in a state of rest or uniform motion unless there are forces acting on it. • No external force means no change in velocity • Second Law • A net force F acting on a body of mass m [kg] produces an acceleration a = F /m [ms-2] • Relates motion to its cause F = maunits of F: kg.m.s-2, called Newtons [N]

  8. Fb • Force exerted by block on table is Fa • Force exerted by table on block is Fb Block on table • Third Law • The force exerted by A on B is equal and opposite to the force exerted by B on A Fa Fa=-Fb Weight (a Force) (Both equal to weight) Examples of Forces For this course: weight of body from gravity (mg), tension, compression Friction,

  9. Tension & Compression • Tension • Pulling force - flexible or rigid • String, rope, chain and bars • Compression • Pushing force • Bars • Tension & compression act in BOTH directions. • Imagine string cut • Two equal & opposite forces – the tension mg mg mg

  10. Friction • A contact force resisting sliding • Origin is chemical forces between atoms in the two surfaces. • Static Friction (fs) • Must be overcome before an objects starts to move • Kinetic Friction (fk) • The resisting force once sliding has started • does not depend on speed N fs or fk F mg

  11. From Benson, University Physics, Revised Addition Questions • Topics Covered • Vector addition and dot product, descriptions of motion, Newton’s 3 laws, Friction.

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