AP Physics C Mechanics- 2.4 Newton’s First Law- Study Notes- New Syllabus
AP Physics C Mechanics- 2.4 Newton’s First Law – Study Notes
AP Physics C Mechanics- 2.4 Newton’s First Law – Study Notes – per latest Syllabus.
Key Concepts:
Net Force on a System
The net force acting on a system is the vector sum of all individual forces exerted on it by the environment. Each force is considered with both magnitude and direction, and the vector addition of all these determines the system’s overall motion.
\( \mathrm{\sum \vec{F}_{net} = \vec{F}_1 + \vec{F}_2 + \vec{F}_3 + \cdots} \)
- The net force determines the acceleration of the system: \( \mathrm{\sum \vec{F}_{net} = M\vec{a}_{cm}} \).
- If forces are unbalanced, the system accelerates in the direction of the net force.
Example
A block on a horizontal surface is pulled to the right by \( \mathrm{10\,N} \) and opposed by a frictional force of \( \mathrm{4\,N} \). Find the net force acting on it.
▶️ Answer / Explanation
\( \mathrm{F_{net} = F_{applied} – F_{friction} = 10 – 4 = 6\,N.} \)
The block experiences a net force of \( \mathrm{6\,N} \) to the right, causing acceleration in that direction.
Translational Equilibrium
A system is said to be in translational equilibrium when the net force on it is zero. This means all the forces acting on the system cancel out, resulting in no linear acceleration.
Derived Equation:
\( \mathrm{\sum \vec{F}_{t} = 0} \)
- If the object is at rest, it remains at rest.
- If the object is in motion, it continues to move at a constant velocity.
- Equilibrium can occur in one, two, or three dimensions depending on the forces involved.
Example
A hanging lamp is supported by two strings attached symmetrically to the ceiling. The lamp is at rest.
▶️ Answer / Explanation
The vertical components of the tension forces balance the lamp’s weight, and the horizontal components cancel each other:
\( \mathrm{\sum F_x = 0,\quad \sum F_y = 0.} \)
Hence, the lamp is in translational equilibrium.
Newton’s First Law of Motion
Newton’s First Law states that if the net external force acting on a system is zero, the system’s velocity remains constant. This includes both stationary systems and those moving with uniform velocity.
\( \mathrm{\sum \vec{F}_{net} = 0 \Rightarrow \vec{a} = 0 \Rightarrow \text{constant } \vec{v}} \)
- It defines the condition of equilibrium and the nature of inertial motion.
- The law introduces the concept of inertia — the tendency of an object to resist changes in motion.
Example
A hockey puck slides across smooth ice at constant speed until friction from the surface gradually slows it down.
▶️ Answer / Explanation
When the puck glides frictionlessly, the net force on it is zero, so it continues at constant velocity — demonstrating Newton’s First Law. Once friction acts, the net force is no longer zero, causing the puck to decelerate.
Force Balance in Multiple Dimensions
Forces can be balanced in one direction while unbalanced in another. An object’s velocity will change only in the direction where the net force is nonzero.
- Force components along each coordinate axis must be considered independently.
- Translational equilibrium occurs only when net force components are zero along all directions.
Mathematical condition:
\( \mathrm{\sum F_x = 0,\quad \sum F_y = 0,\quad \sum F_z = 0.} \)
Example
A block slides down a frictionless incline. Along the surface, gravity is unbalanced, but perpendicular to the surface, forces are balanced.
▶️ Answer / Explanation
Gravity has components:
\( \mathrm{F_{g\parallel} = mg\sin\theta} \quad \text{(unbalanced)} \)
\( \mathrm{F_{g\perp} = mg\cos\theta} \quad \text{(balanced by } F_N\text{)} \)
Thus, the block accelerates down the incline but remains in equilibrium perpendicular to the plane.
Inertial Reference Frames
An inertial reference frame is a frame of reference in which Newton’s First Law holds true. In such frames, an object not acted upon by a net external force moves with constant velocity or remains at rest.
- Inertial frames are either stationary or moving at constant velocity.
- Accelerating or rotating frames are non-inertial — in these, fictitious (pseudo) forces must be introduced to explain motion.
- All inertial frames are equivalent for the laws of mechanics.
Example
A passenger inside a car moving at a constant velocity tosses a ball straight up, and it lands back in their hand.
▶️ Answer / Explanation
To the passenger (in the car’s frame), the ball appears to move vertically up and down — this is an inertial frame. However, if the car accelerates, the ball appears to move backward — this shows that the car has become a non-inertial frame.