The position vector of a particle of mass 2kg is given as a function of time by r=6i+5tj.determine the angular momentum of the particle about the origin as a function of time
The angular momentum of a particle about the origin is given by the cross product of the position vector (r) and the linear momentum vector (p) of the particle.
The linear momentum vector is given by p = m*v, where m is the mass of the particle (2kg) and v is the velocity vector of the particle given by the derivative of the position vector with respect to time: v = dr/dt = 5j.
Therefore, the linear momentum vector is p = 2*5j = 10j.
Now, we can calculate the angular momentum L as:
L = r x p = (6i + 5tj) x 10j
= 10t*k
Therefore, the angular momentum of the particle about the origin as a function of time is L = 10t*k.