Question

1. Consider a particle of mass M moving on a two dimensional plane. It is subjected to a constant attractive central force F directed towards the origin and has an angular momentum L w.r.t the origin. a) Draw the Effective Potential Diagram qualitatively and indicate on the diagram at what radius circular motion is possible. 10 b) In the same diagram, for a given energy E, identify the maximum and minimum radius accessible by the particle. 5 c) Suppose the particle's mass M is 1kg. At time t=0, it is at a radius r0=1m and has angular velocity ?0 = 1 rad/sec, with radial velocity zero. The value of force F=2 N. What is the radius of closest approach to the origin in the subsequent motion? 10

          1. Consider a particle of mass M moving on a two dimensional plane. It is subjected to a
constant attractive central force F directed towards the origin and has an angular
momentum L w.r.t the origin.
a) Draw the Effective Potential Diagram qualitatively and indicate on the diagram at
what radius circular motion is possible.
10
b) In the same diagram, for a given energy E, identify the maximum and minimum
radius accessible by the particle.
5
c) Suppose the particle's mass M is 1kg. At time t=0, it is at a radius r0=1m and has
angular velocity ?0 = 1 rad/sec, with radial velocity zero. The value of force F=2
N. What is the radius of closest approach to the origin in the subsequent
motion?
10

1. Consider a particle of mass M moving on a two dimensional plane. It is subjected to a
constant attractive central force F directed towards the origin and has an angular
momentum L w.r.t the origin.
a) Draw the Effective Potential Diagram qualitatively and indicate on the diagram at
what radius circular motion is possible.
10
b) In the same diagram, for a given energy E, identify the maximum and minimum
radius accessible by the particle.
5
c) Suppose the particle's mass M is 1kg. At time t=0, it is at a radius r0=1m and has
angular velocity ?0 = 1 rad/sec, with radial velocity zero. The value of force F=2
N. What is the radius of closest approach to the origin in the subsequent
motion?
10

Added by Michael J.

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