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## Class 11 Physics (India)

### Unit 9: Lesson 2

Newton's first law: Mass and inertia

# What is Newton's first law?

Also called the law of inertia, this is the most important thing to realize about motion.

## Why do objects slow down?

Before Galileo and Newton, many people thought objects slowed down because they had a natural built in tendency to do so. But those people weren't taking into account the many forces—e.g., friction, gravity, and air resistance—here on Earth that cause objects to change their velocity. If we could observe the motion of an object in deep interstellar space, we would be able to observe the natural tendencies of an object's motion free from any external influences. In deep interstellar space, we would observe that if an object had a velocity, it would continue moving with that velocity until there was some force to cause a change in the motion. Similarly, if an object were at rest in interstellar space, it would remain at rest until there was a force to cause it to change its motion.
In the video below, we can see that objects in the international space station either remain at rest or continue with constant velocity relative to the space station until acted upon by a force.
The idea that objects only change their velocity due to a force is encapsulated in Newton's first law.
Newton's first law: An object at rest remains at rest, or if in motion, remains in motion at a constant velocity unless acted on by a net external force.
Note the repeated use of the verb remains. We can think of this law as preserving the status quo of motion. Newton’s first law of motion states that there must be a cause—which is a net external force—for there to be any change in velocity, either a change in magnitude or direction. An object sliding across a table or floor slows down due to the net force of friction acting on the object. But on an air hockey table, where air keeps the puck from touching the table, the air hockey puck continues moving with a roughly constant velocity until a force acts on it—like when it bumps into the side of the table.

## What do force, external force, and net force mean?

A force is a push or a pull exerted on one object by another object. The units of force F are called Newtons or simply start text, N, end text.
An external force is a force originating from outside an object rather than a force internal to an object. For instance, the force of gravity that Earth exerts on the moon is an external force on the moon. However, the force of gravity that the inner core of the moon exerts on the outer crust of the moon is an internal force on the moon. Internal forces within an object can't cause a change in that object's overall motion.
The net force, written as \Sigma, F, on an object is the total force on an object. If many forces act on an object, then the net force is the sum of all the forces. But be careful—since force F is a vector, to find the net force \Sigma, F, the forces must be added up like vectors using vector addition.
In other words, if a box of frozen burritos had a force of magnitude 45 Newtons exerted on it to the right and a force of magnitude 30 Newtons exerted on it to the left, the net force in the horizontal direction would be
\Sigma, F, start subscript, start text, h, o, r, i, z, o, n, t, a, l, end text, end subscript, equals, 45, start text, space, N, end text, minus, 30, start text, space, N, end text
\Sigma, F, start subscript, start text, h, o, r, i, z, o, n, t, a, l, end text, end subscript, equals, 15, start text, space, N, end text
Assuming rightward is the positive direction.
Newton's first law says that if the net force on an object is zero (\Sigma, F, equals, 0), then that object will have zero acceleration. That doesn't necessarily mean the object is at rest, but it means that the velocity is constant. In other words, constant zero velocity—at rest—or constant non-zero velocity—moving with a constant velocity.
For the box of frozen burritos, if the rightward force had a magnitude of 45 Newtons and the leftward force had a magnitude of 45 Newtons, the net force would be zero. The box of burritos would either continue moving with a constant velocity—if it started with a velocity before the forces were applied—or stay at rest—if it was already at rest before the forces were applied.

## What does mass mean?

The property of a body to remain at rest or to remain in motion with constant velocity is called inertia. Newton’s first law is often called the law of inertia. As we know from experience, some objects have more inertia than others. It is obviously more difficult to change the motion of a large boulder than that of a basketball, for example.
The inertia of an object is measured by its mass. Mass can be determined by measuring how difficult an object is to accelerate. The more mass an object has, the harder it is to accelerate.
Also, roughly speaking, the more “stuff”—or matter—in something, the more mass it will have, and the harder it will be to change its velocity, i.e., accelerate.

## What do solved questions involving Newton's first law look like?

### Example 1: space probe drift

A space probe is drifting to the right at a constant velocity in deep interstellar space—far from any influence due to planets and stars—with its rockets off. If two rocket thrusters both turn on simultaneously exerting identical forces leftward and rightward in the directions shown, what would happen to the motion of the rocket?
a. The space probe would continue with constant velocity.
b. The space probe would speed up.
c. The space probe would slow down and eventually stop.
d. The space probe would immediately stop.
The correct answer is a. According to Newton's first law, a non-zero net force is required to change the velocity of an object. The net force on the space probe is zero—since the forces on it cancel—so there is no change in the velocity of the probe.

### Example 2: elevator lift

An elevator is being pulled upward at a constant velocity by a cable as seen in the diagram below. While the elevator is moving upward at constant velocity, how does the magnitude of the upward force exerted on the elevator by the cable—start color #e84d39, F, start subscript, c, end subscript, end color #e84d39—compare to the magnitude of the downward force of gravity—start color #1fab54, F, start subscript, g, end subscript, end color #1fab54—on the elevator?
a. start color #e84d39, F, start subscript, c, end subscript, end color #e84d39 is greater than start color #1fab54, F, start subscript, g, end subscript, end color #1fab54.
b. start color #e84d39, F, start subscript, c, end subscript, end color #e84d39 is equal to start color #1fab54, F, start subscript, g, end subscript, end color #1fab54.
c. start color #e84d39, F, start subscript, c, end subscript, end color #e84d39 is smaller than start color #1fab54, F, start subscript, g, end subscript, end color #1fab54.
d. start color #e84d39, F, start subscript, c, end subscript, end color #e84d39 could be larger or smaller than start color #1fab54, F, start subscript, g, end subscript, end color #1fab54 depending on the mass of the elevator.
The correct answer is b. If the elevator is moving with constant velocity, the net force must be zero. In order for the net force on the elevator to be zero, the upward and downward forces must cancel exactly.

### Example 3: space probe path

A space probe is drifting to the right with constant velocity in deep interstellar space—far from any influence due to planets and stars. If a rocket thruster turns on and then off for a short burst of force in the direction shown, what would best represent the path traveled by the rocket after the thruster turns off?
a. Path a
b. Path b
c. Path c
d. Path d
The correct answer is c. After the rocket thruster turns off, there will be no net force on the space probe. Once the net force is zero, the velocity—both magnitude and direction—must be constant. Because of Newton's first law, the space probe moves in a straight line at constant speed. The fact that there was a vertical force on the space probe does not affect the horizontal velocity of the space probe, it only changes the vertical velocity. A constant vertical and horizontal velocity yields a diagonal straight line through space.