Laws of motion: Physics Notes for PSU Jobs (via GATE)

Laws of Motion – Study Notes

(Physics – PSU‑Jobs, GATE Preparation)

1. Simple Explanation

Newton’s Three Laws of Motion describe how objects move when forces act on them.
They form the foundation of classical mechanics and are used everywhere in physics, engineering and everyday life.

Law	What it states
1st	An object remains at rest or in uniform motion unless acted upon by a net external force.
2nd	The acceleration of an object is proportional to the net force acting on it and inversely proportional to its mass. ( \mathbf{F}_{\text{net}} = m\mathbf{a} ).
3rd	For every action there is an equal and opposite reaction.

2. Key Points

#	Concept	Why it matters (GATE relevance)
1	Inertial frames – Newton’s laws hold in frames that are not accelerating.	Most GATE questions assume inertial frames unless stated otherwise.
2	Net force – vector sum of all external forces.	Must be careful to include all forces (tension, gravity, normal, friction, air‑drag).
3	Mass (m) – property of matter, constant.	Appears in 2nd law; helps compare accelerations of different bodies.
4	Acceleration (a) – change in velocity per unit time.	GATE often asks for (a) when forces are given, or vice‑versa.
5	Action‑reaction pairs – always internal to the system.	Important when analyzing multiple bodies connected by strings or springs.
6	Free‑body diagrams (FBD) – essential first step.	GATE problems frequently test your ability to draw correct FBDs.
7	Friction & normal forces – often secondary but crucial.	Many PSU‑Jobs problems involve inclined planes, blocks, or rolling objects.
8	Conservation of momentum – direct consequence of 3rd law.	Useful for collisions, explosions, or systems with no external forces.

3. Worked Example

Problem (typical GATE style):
A 3 kg block is pulled on a horizontal frictionless table by a string that is attached to a 5 kg block hanging over a smooth pulley. The string is taut. Find the acceleration of each block and the tension in the string.

Step‑by‑step solution

Identify the system & free‑body diagrams
- Block A (3 kg) on table: only horizontal force is tension (T).
- Block B (5 kg) hanging: forces are weight (W = mg = 5g) downward and tension (T) upward.
Choose coordinate system
- Positive (x) is to the right (direction of motion of block A).
- Positive (y) is upward.
Apply Newton’s 2nd law to each block
- Block A (horizontal)
  [ T = m_A a \quad\Rightarrow\quad T = 3a \tag{1} ]
- Block B (vertical)
  [ m_B g - T = m_B a \quad\Rightarrow\quad 5g - T = 5a \tag{2} ]
Solve the simultaneous equations
Substitute (T = 3a) from (1) into (2):

[ 5g - 3a = 5a \quad\Rightarrow\quad 5g = 8a \quad\Rightarrow\quad a = \frac{5g}{8} ]

Using (g = 9.8\ \text{m s}^{-2}):

[ a \approx \frac{5 \times 9.8}{8} = 6.125\ \text{m s}^{-2} ]
Find the tension
[ T = 3a = 3 \times 6.125 \approx 18.4\ \text{N} ]

Answers

Acceleration of each block: (6.13\ \text{m s}^{-2}) (Block A to the right, Block B downward).
Tension in the string: (18.4\ \text{N}).

4. Quick Revision Summary

Concept	Remember
1st Law	Inertia – no net force → no change in motion.
2nd Law	( \mathbf{F}{\text{net}} = m\mathbf{a} ). Solve for (a) or (F{\text{net}}).
3rd Law	Action and reaction forces are equal in magnitude, opposite in direction.
Free‑body diagram	Draw all external forces; keep them as vectors.
Inertial frame	If the reference frame is accelerating, add fictitious “inertial” forces.
Conservation of momentum	(\sum m v = \text{constant}) when no external forces act.
Common pitfalls	- Neglecting friction or normal forces. - Mixing up directions of forces. - Forgetting that action‑reaction pairs act on different bodies.
GATE practice tip	For every problem: (a) Sketch a clear FBD, (b) Write equations for each body, (c) Solve simultaneously, (d) Check units & sign convention.

Final Note

Mastering Newton’s laws is the first step toward understanding dynamics, statics, and advanced topics like rotational motion and non‑inertial reference frames. Keep practicing with diverse problems—especially those that involve multiple bodies or constraints—to build intuition and speed for the PSU‑Jobs (via GATE)