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, we first need to find the velocity vector and then calculate the angular momentum using the formula:
Angular momentum = r x (mv)
Given position vector r = 6i + 5tj, the velocity vector v is the derivative of r with respect to time t:
v = dr/dt = d(6i + 5tj)/dt = 0i + 5j
Now, calculate the angular momentum as a function of time t:
r x (mv) = (6i + 5tj) x (0i + 5j)
= (0*j - 5t*i)k
= -5t*k
Therefore, the angular momentum of the particle about the origin as a function of time is -5t*k.