Newton's First Law of Inertia 🐘

**Newton’s First Law states, “every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed on it.” **

Another term for this law is the Law of Inertia because it explains the concept that objects have the tendency to resist a change in motion. It is also commonly referred to as just a special case of Newton’s Second Law when the net external force is zero. 

Key Concept: Frame of Reference: A coordinate system in relation to which judgments can be made, usually from an observer’s point of view, is known as a frame of reference. A frame of reference moving with constant velocity is known as an inertial frame of reference. 

Key Concept: Inertial Mass - the ability of an object to resist a change in its state of motion. The inertia of an object is measured based on its mass. 

An object with a small mass will exhibit less inertia and be more affected by other objects, and an object with a large mass will exhibit greater inertia and be less affected by other objects. That’s why it would be a lot harder to move an elephant from rest than an ant! Simply put, inertial mass is a measure of how difficult it is to change the uniform motion of an object by an external force. (🐜 < 🐘)

Image courtesy of WikiHow.

As shown in the image above, the force of the person, given by mass x acceleration, is equal to Fnet because it is the only unbalanced force. However, if the sum of the forces acting on the object is zero then the system would be in equilibrium.  Key Concept: Equilibrium - when the vector sum of the forces acting on an object is equal to zero

Example Problem #1: 

A student is sitting in a classroom at rest. The student's desk is pushed by a classmate, causing the student and desk to start moving across the room. The student's teacher then pushes the student and desk back in the opposite direction.

1. What is the external force acting on the student and desk?
2. How does the student's inertia affect their motion?
3. If the student's teacher pushes the student and desk with a greater force, what will happen to the student's motion?
4. How does the mass of the student and desk affect their motion?

1. The external force acting on the student and desk is the push from the classmate and the push from the teacher.

1. The student's inertia affects their motion by causing them to resist a change in their motion. When the student and desk are at rest, they will remain at rest unless an external force is applied to them. When the student and desk are moving, they will continue to move at a constant velocity unless an external force is applied to them.

1. If the student's teacher pushes the student and desk with a greater force, the student and desk will accelerate in the direction of the force. The greater the force, the greater the acceleration will be.

1. The mass of the student and desk affects their motion because objects with more mass are harder to accelerate than objects with less mass. This is due to the fact that the force required to accelerate an object is proportional to its mass. So, if the student and desk have a greater mass, they will be harder to accelerate, and if they have a smaller mass, they will be easier to accelerate.

Example Problem #2:

Design an experiment to determine the relationship between the net force exerted on a small wooden block, its inertial mass, and its acceleration.

Identify the variables: 

• Independent variable: net force applied to the object

• Dependent variables: inertial mass of the object, acceleration of the object Determine the experimental setup:

• Device to apply force to the object: spring scale, force sensor

• Way to measure the inertial mass of the object: balance scale

• Way to measure the acceleration of the object: timer, photogate Determine the experimental procedure:

1. Measure the inertial mass of the object using the balance scale.
2. Apply a series of increasing forces to the object using the spring scale or force sensor.
3. Measure the acceleration of the object using the timer or photogate.
4. Record the values of the force, inertial mass, and acceleration for each trial. Analyze the data:

• Plot the values of the force, inertial mass, and acceleration on a graph.

• Examine the relationship between the three variables. Draw conclusions:

• The net force applied to an object is directly proportional to its acceleration.

• The inertial mass of the object is a measure of its resistance to acceleration.

• The relationship between the force, inertial mass, and acceleration follows the equation F=ma, where F is the force, m is the inertial mass, and a is the acceleration.

Gravitational vs Inertial Mass 🐁

Objects and systems have properties of inertial mass and gravitational mass that are experimentally verified to be the same and that satisfy conservation principles.

Key Concept: Gravitational Mass - determined by the strength of the gravitational force experienced by the body when in the gravitational field g.

Equation:

Gravitational Mass vs. Inertial Mass

• Gravitational mass is measured by comparing the force of gravity of an unknown mass to the force of gravity of a known mass.
• Inertial mass is found by applying a known force to an unknown mass, measuring the acceleration, and applying Newton's Second Law, a = F/m. Equation:

While these masses are measured in varying applications, they have been experimentally proven to equal the same value; therefore Inertial = Gravitational 

Key things to remember:

• Gravitational mass is a measure of the amount of matter in an object. It determines how much the object is attracted to other objects with mass due to the force of gravity.
• Inertial mass is a measure of the resistance of an object to acceleration. It determines how difficult it is to change the velocity of an object, whether by pushing, pulling, or any other force.
• Both gravitational mass and inertial mass are properties of matter, and they are usually considered to be the same. In other words, an object with a large gravitational mass will also have a large inertial mass, and vice versa.
• However, there are some interesting situations in which gravitational mass and inertial mass may not be exactly equal. For example, in Einstein's theory of relativity, the two masses can be slightly different due to the effects of gravity on time and space.

Watch: AP Physics 1 - Unit 2 Streams

Example Problem:

You have been asked to design a plan for collecting data to measure both the gravitational mass and the inertial mass of a golf ball. You will also need to determine whether the golf ball has the same gravitational mass and inertial mass, or if they are different.

Part A: Explain the difference between gravitational mass and inertial mass.

Part B: Describe how you would design an experiment to measure the gravitational mass of the golf ball. Be sure to include all necessary materials, procedures, and any calculations you would need to make in order to compare the gravitational mass to the inertial mass.

Part C: Describe how you would design an experiment to measure the inertial mass of the golf ball. Be sure to include all necessary materials, procedures, and any calculations you would need to make in order to compare the inertial mass to the gravitational mass.

Part D: Explain how you would use the data collected in your experiments to determine whether the golf ball has the same gravitational mass and inertial mass, or if they are different.

Part E: Discuss any potential sources of error in your experiments and how you would minimize or correct them.