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
To find the angular momentum of the particle about the origin as a function of time, we first need to find the velocity vector and the momentum vector.
The velocity vector v is given by the derivative of the position vector with respect to time:
v = dr/dt = (0)i + 5j
The momentum vector p is given by the mass times the velocity vector:
p = m*v = 2*(0)i + 10j = 10j
The angular momentum L about the origin is given by the cross product of the position vector and the momentum vector:
L = r x p = (6i + 5tj) x 10j
= (0)i x 10j + (6i x 10j + 5tj x 10j)
= 60i + 50t(-k) = 60i - 50tk
Therefore, the angular momentum of the particle about the origin as a function of time is given by:
L = 60i - 50tk.