# Relationship between momentum and inertia

by samclocks
Tags: inertia, momentum, relationship
 P: 2 1. The problem statement, all variables and given/known data So, let's say a car is rolling down a ramp. I have to maximize its acceleration, but I am confused about some things. I think that if I increase the car's mass, then it will have more momentum and roll down the ramp faster. But according to Newton's First Law of Motion, an object's mass is inversely proportional to its acceleration. Its saying that having more mass will slow down the car's acceleration. So to me, these two things are contradicting to each other. Should I increase the mass, or decrease the mass of the car to make it roll down the ramp faster? 2. Relevant equations 3. The attempt at a solution
HW Helper
P: 6,684
 Quote by samclocks 1. The problem statement, all variables and given/known data So, let's say a car is rolling down a ramp. I have to maximize its acceleration, but I am confused about some things. I think that if I increase the car's mass, then it will have more momentum and roll down the ramp faster. But according to Newton's First Law of Motion, an object's mass is inversely proportional to its acceleration. Its saying that having more mass will slow down the car's acceleration. So to me, these two things are contradicting to each other. Should I increase the mass, or decrease the mass of the car to make it roll down the ramp faster?
Your question is one that scientists before Galileo argued about. Galileo showed that all objects dropped from the same height take the same time to reach the ground. This means that all objects have the same acceleration due to gravity.

Newton showed that F = ma or a = F/m.

So if acceleration, a, is the same for all objects (about 9.8 m/sec^2) what does that say about the relationship between the force of gravity and mass?

AM
 P: 2 So no matter what the car's mass is, the acceleration will be always 9.8m/sec^2 when rolling down the ramp?