2Consider a particle of mass m moving in two dimensions (neglect gravity). The particle feels acentral force given by F = m². Here is a positive constant, î= is a unit vector and r isthe position of the particle.a) How many degrees of freedom does the system have?bmb) State the conserved quantities and find the corresponding Noether symmetries.c) Find expressions for the conserved quantities in terms of polar coordinates r, 0.

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Consider a particle of mass m moving in two dimensions (neglect gravity). The particle feels a central force given by F = -f. Here is a positive constant, is a unit vector and r is 7 the position of the particle. O r a) How many degrees of freedom does the system have? b b) State the conserved quantities and find the corresponding Noether symmetries. c) Find expressions for the conserved quantities in terms of polar coordinates r, 0.

Consider a particle of mass m moving in two dimensions (neglect gravity). The particle feels a central force given by F = -f. Here is a positive constant, is a unit vector and r is 7 the position of the particle. O r a) How many degrees of freedom does the system have? b b) State the conserved quantities and find the corresponding Noether symmetries. c) Find expressions for the conserved quantities in terms of polar coordinates r, 0.