If you have any sense of style the first object you test your engine with should be an apple
Writing a full blown physics engine can take some time so here are the ones used by people who hate math.
Box2D - 2007
Box2D C++ tutorials - Introduction - 2011
Bullet - 2005
Newton Dynamics - 2004
PhysX - 2004
NVIDIA® PhysX® SDK Documentation 3.3.1
NVIDIA(R) PhysX(R) SDK 3.3.1 API Reference
APEX Clothing Module - 1.3.1
PhysX Knowledge Base/FAQ
PhysX Dynamic Heightfield Modifications - 2014
ODE - 2001
Havok - 2000