Q.a) A balloon of mass m is descending with an acceleration α. What mass should be dropped from the balloon so that it starts moving upward with the same acceleration α? b) Define inertial frame of reference. OR Define centripetal force. A particle of mass m is rotating around a circular path of radius r. Find the centripetal acceleration of the particle and the magnitude and direction of the centripetal force acting on it.

Newton's laws are the three rules that tell you how forces change motion. They are the foundation of the whole Laws of Motion unit: every later idea — friction, pulleys, circular dynamics, pseudo-forces — is just these three laws applied to a particular situation.

1 — First law (inertia). A body keeps its state of rest or of uniform motion in a straight line unless a net external force acts on it. Inertia is this reluctance to change velocity; its measure is the mass. The first law also defines an inertial frame — one in which a force-free body has no acceleration. A frame that is itself accelerating is non-inertial, and Newton's laws hold there only after adding a pseudo-force (a separate concept).

2 — Second law. The net force equals the rate of change of momentum:

F_net = dp/dt, and for constant mass p = mv gives the working form F_net = ma.

Force is a vector, so this is really ΣF_x = ma_x and ΣF_y = ma_y. If several concurrent forces act on one body, first add them as vectors to get F_net, then a = F_net/m. The SI unit is the newton: 1 N = 1 kg·m/s². Because F = ma sets the acceleration, it links directly to kinematics (v = u + at, s = ut + ½at²): a constant force ⇒ constant acceleration.

3 — Third law. Every force comes in a pair: if A pushes B with force F, then B pushes A with −F. The two forces are equal in magnitude, opposite in direction, and act on different bodies — which is exactly why they do not cancel (they never act on the same object). A common trap: a book's weight and the normal reaction on it are not a third-law pair (both act on the book, and one is gravity while the other is contact); the true reaction to the book's weight is the pull the book exerts on the Earth.

Types of force you will meet. Weight W = mg (always vertically down; g changes the weight but never the mass). Normal reaction N — perpendicular to a surface, whatever value is needed to prevent interpenetration (on a horizontal floor N = mg with no other vertical force, but N = mg + F if you also push down and N = mg − F if something pulls up). Tension in a string, applied/contact forces, and the spring force F = kx (proportional to the stretch/compression). Mass is the scalar amount of matter (same everywhere); weight is the gravitational force on it (varies with location) — keep the two separate. …