Overcoming the inertia of a body at rest

Neglecting friction and other forces (air resistance) and assuming all forces are orthogonal the gravity vector , consider a large dense sphere at rest on a perfectly flat plane which is plumb. Now for the sake of simplicity, let us say the inertia of the sphere is 1 kg/m2. What happens when a force of less than the sphere's inertia is applied to the sphere? And if a force greater than the sphere's inertia is applied, will it move instantly at the velocity of the applied force, or will the velocity of the applied force dictate the period during which inertia is overcome, prior to the sphere's movement?

• I tried to provide breaks in the text to make it more readable, but it posted without breaks. Really need some help on this one, though! Aug 10, 2018 at 16:15
• "let us say the inertia of the sphere is 1 kg/m2" - inertia has dimension of (inertial) mass with SI unit $\mathrm{kg}$. Aug 10, 2018 at 16:21
• "What happens when a force of less than the sphere's inertia is applied to the sphere? " - force equals the product of mass and acceleration. What do you mean by "a force less than the sphere's inertia"? Aug 10, 2018 at 16:22
• @RaSullivan - to start a new paragraph, leave two empty lines between text. See the formatting help for more information. Aug 10, 2018 at 18:27
• Note that there is no such thing as a "velocity of the applied force". Force does not cause a specific velocity, it causes a specific acceleration. A particular force can cause any velocity depending on duration and initial situation - there is no single particular velocity associated with a force. Aug 11, 2018 at 6:41

Neglecting friction and air resistence completely, there is no such thing as "overcoming inertia." Any external force acting on an object with mass, even if it a person pushing on the planet Earth, will cause it to accelerate, though inversely proportional to its mass (so really really small). Inertia is this concept of how much a force inversely affects acceleration, which is directly proportional to mass. It does not have units of kg/m^2

When "overcoming inertia" causes something unmoving to move, you are actually overcoming static friction.

Also note that a sphere cannot roll without friction, so it would just slide. In your example, no matter what, the sphere will slide if you push on it.

• "overcoming inertia" is a common phrase used by people first learning physics. It is a really understood concept. I think you did a good job addressing it by saying the misconception might be due to people thinking about friction. I hadn't thought of that before. Aug 10, 2018 at 16:28
• Yep, this is the common understanding of Aristotelian mechanics Aug 10, 2018 at 16:37
• Oops I meant to say "misunderstood" Aug 10, 2018 at 16:40
• Aron and Duncan, I don't think you get it. Many don't. It's deeper than recited text. Aug 11, 2018 at 3:10
• Additionally Aron, how do u know when I started learning anything? A little full of yourself, I'd say. Just my opinion. Aug 11, 2018 at 3:14

You don't have to "overcome inertia". Inertia is not something to overcome.

Inertia only slows down the acceleration which a force causes. But it doesn't prevent it. It doesn't give any lower limit that must be overcome. Look at Newtons 2nd law with mass $m$ being the inertia of the object that is pushed upon:

$$\sum F=ma$$

The tiniest force would cause a tiny acceleration. With a high inertia, the acceleration would be even smaller - but not zero.

The sphere you describe will start movig at any tiny force being applied.

• If inertia offers any resistance to the movement of the object, your answer doesn't work for me. Aug 11, 2018 at 3:09
• @RaSullivan I am sorry, I don't understand your comment. Did I miss the point of your question? The answer to your question as is, is that any force, no matter the size, will speed up the object. With a higher inertia, this speeding-up just happens gradually slower. But it still happens, no matter the size of the force. There is no "threshold" or "limit" that must be overcome. Aug 11, 2018 at 6:18