Question

The position vector of a particle of mass 1.65 kg as a function of time is given by = (6.00 î + 4.15 t ĵ), where is in meters and t is in seconds. Determine the angular momentum of the particle about the origin as a function of time.

Answer 1

L = 41.09 Kg m2 / s The angular momentum does not depend on the time

Step-by-step explanation:

The definition of angular momentum is

L = r x p

Where blacks indicate vectors

Let's apply this definition our case. Linear momentum

p = m v

Let's replace

L = m r x v

The given function is

x = 6.00 i ^ + 4.15 t j ^

We look for speed

v = dx / dt

v = 0 + 4.15 j ^

To evaluate the angular momentum one of the best ways is to use determinants

`L = m \left[\begin{array}{ccc}i&j&k\\6&4.15t&0\\0&4.15&0\end{array}\right]`

L = m 6 4.15 k ^

The other products give zero

Let's calculate

L = 1.65 6 4.15 k ^

L = 41.09 Kg m2 / s

The angular momentum does not depend on the time