Classical Mechanics
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[edit] Kinematics / Short Problems
- How fast (in terms of the original velocity) would a bowling ball be moving at when it starts rolling without slipping, if thrown on a surface with μ and no initial spin?
- A small object rests on the edge of a 1m horizontal table. It is given a push (initial velocity) such that it gets to the other side table after 2s. Does the object have wheels?
General formula for small oscillations in one dimension
- Show that frequency for small oscillations can be expressed simply as the second derivative of the potential.
[edit] Kinematics / Long Problems
Two masses on rods connected by springs
- Two masses are each connected to a massless rod and joined by a spring, what is the freq. of small oscillations?
- What is the frequency of small oscillations of a ball rolling without slipping on a table, attracted by a force that is proportional to r ?
- A block of mass m slides without friction on an inclined plane of angle α and mass M that rests of a frictionless horizontal surface. The block is constrained to sit on the incline. Using Lagrange's equations, find the equations of motion of the block and the inclined plane.
- A different approach to the familiar Lagragian problem.
- What are the equations of motion for a pencil falling from an upright position on a frictionless surface?
- What would a box look like moving at relativistic speeds?
[edit] Other
- A small collection of GRE problems/solutions
