# Similarity between velocity and momentum

1. Dec 17, 2015

### kaushikquanta

as momentum is product of mass and velocity ,it is a vector quantity but mass is a scalar.when a scalar is multiplied to a vector ,it's magnitude increases .then there must certain similarities between velocity and momentum.

2. Dec 17, 2015

### RUber

The similarity is that the vectors are collinear, i.e. they share the same unit vector. Also, the magnitude only increases if the scalar (mass) is greater than 1.
Also, since acceleration is the change in velocity, force is the change in momentum if you assume mass to be constant.
$A = \frac{d}{dt}V$
$F=mA = m\frac{d}{dt}V=\frac{d}{dt}(mV)$

3. Dec 17, 2015

### jbriggs444

Since mass is not a unitless quantity, whether it is greater or less than one depends on one's choice of units. It is arbitrary. Since momentum and velocity are not unitless quantities, whether one has larger magnitude than the other also depends on one's choice of units. It is also arbitrary.

The comparison of magnitudes seems pointless. It is like asking whether an apple is rounder than an orange is tall.

Last edited: Dec 17, 2015