Final exam: room 105 HECC, 8-10 am, Wednesday, December 12 th

Kinematics is given, you can find If and

Kinematics of circular motion is given, you can find If and by integration, similarly to linear motion

General motion y x

Newton’s First Law Second Law Third Law Dynamics I

A Recipe for Solving Problems 1.Sketch Isolate the body (only external forces but not forces that one part of the object exert on another part); Identify all forces, maybe using 3 rd law 2. Write down 2 nd Newton’s law Choose a coordinate system Write 2 nd Newton’s law in component form: 3. Solve for acceleration, then integrate You can use different coordinates for different bodies, but be careful to relate them properly.

For rigid bodies rotating about their axis of symmetry: Second Law: m1 m2 R Dynamics of rotational motion

Kinetic energy of a rigid body or an ensemble of particles Applications: rolling without slipping, combined rotational and translational motion Rotation of a rigid body about a fixed point O:

Conservation laws: shortcuts to find velocities bypassing Newton’s law and accelerations Momentum Angular momentum energy

Work Energy Theorem

does NOT depend on path!

Mechanical energy is conserved! Know examples of conservative and non-conservative forces If an unknown force depends only on a coordinate, it is probably conservative

Conservation of Momentum If the collision is perfectly elastic, the kinetic energy is conserved! Sometimes only F x or F y may be equal to zero. Then only p x or p y is conserved. If F is not zero, but the collision is very short (F  t is small as compared to change in momentum), you can still use momentum conservation relating moments of time immediately before and after the collision.

Conservation of Angular Momentum For symmetrical objects rotating about their axis of symmetry: Second Law: m1 m2 R

Harmonic Motion A and B – from initial conditions Start from Newton’s laws Derive an equation for a small displacement from equilibrium When a force or a torque is proportional to a displacement from equilibrium, it smells like harmonic motion Can be any coordinate, or angle, or anything