Ch 1Rotational Dynamics — Class 12 Physics, concept-first.

Circular motion is one of the two related-but-different kinds of motion this chapter is built around. When every particle of an object moves in a circle about some point or axis that lies OUTSIDE the…

Circular motion -- whether it is revolution or rotation -- has two characteristics that hold no matter how the motion is produced. First, it is always an ACCELERATED motion.

To describe circular motion quantitatively we use ANGULAR versions of the usual translational kinematic quantities.

Whenever a body performs circular motion, SOME resultant real force must be acting on it, directed towards the centre of the circle -- this resultant force is called the centripetal force (CPF), and i…

Uniform circular motion is not just a textbook abstraction -- it underlies a whole family of everyday and engineering situations.

Consider a car (treated as a particle for simplicity) taking a turn on a FLAT, horizontal, circular road of radius r.

A dramatic application of the same idea is the 'well of death' (or 'wall of death') stunt: a vertical, hollow cylindrical wall of radius r, inside which a vehicle is driven in horizontal circles, its…

Relying on friction to provide the centripetal force has two real drawbacks: friction has an upper limit, and on a real road its value is rarely constant, since road surfaces are never perfectly unifo…

A tiny bob (a point mass) attached to a long, flexible, effectively massless and inextensible string, suspended from a rigid support and made to revolve so that the string sweeps out the surface of a…

Beyond horizontal circular motion, many real situations instead involve VERTICAL circular motion, and these split into two genuinely different categories.

Consider a bob (a point mass) tied to a practically massless, inextensible, flexible string, whirled so that it performs a full vertical circular motion of radius r (the string length), the string rot…

The 'sphere of death' is a well-known circus act in which one or more two-wheeler riders perform circles inside a large hollow sphere.

A vehicle crossing the crest of a convex (arched, hump-shaped) over-bridge is, for a brief instant, undergoing a small piece of vertical circular motion, with the bridge's radius of curvature r playin…

Sections 1.2 to 1.4 treated every rotating or revolving object as a single point particle. But a REAL rigid object -- a door, a flywheel, a disc -- consists of countless particles, all rotating togeth…

A uniform ring is an object whose mass is spread (practically) uniformly around the circumference of a circle -- a two-dimensional object of negligible thickness, like a bangle or a thin metal hoop.

A disc is a two-dimensional, effectively flat, circular object (negligible thickness), said to be UNIFORM if its composition and its mass per unit area are the same everywhere across its surface -- th…

Theoretically calculating a moment of inertia by integration (as in section 1.5.2) is only possible for objects whose mass distribution is mathematically simple enough to integrate.

The standard moment-of-inertia expressions collected in Table 3 (as derived, for example, for the ring and disc in sections 1.5.1-1.5.2) are all about an object's own natural AXIS OF SYMMETRY.

The theorem of parallel axes applies to ANY rigid object (of any shape, not necessarily flat), and requires two axes that are PARALLEL to each other, with (at least) one of the two passing through the…

The theorem of perpendicular axes is more restrictive in its scope: it applies ONLY to a LAMINAR object -- a flat, two-dimensional object of negligible thickness, such as a leaf-like sheet, a ring, a…

In translational mechanics, the two central dynamical quantities are force and (linear) momentum . Rotational mechanics has an exact analogue of momentum too, called angular momentum (or 'moment of li…

To connect angular momentum to the moment of inertia built up in section 1.5, consider once again a rigid object made of N particles of masses at respective perpendicular distances from a fixed axis,…

Just as angular momentum turned out to be (the rotational analogue of ), the same style of argument gives the rotational analogue of Newton's second law, .

Section 1.8 defined angular momentum as . Differentiating this with respect to time (using the product rule, since both and can change with time): Now and (Newton's second law), so Since (any vector c…

Objects like a cylinder, a sphere, or a wheel very commonly perform ROLLING motion -- and PURE rolling (rolling without any slipping at the point of contact) is genuinely a combination of two simultan…

Consider a rigid object of mass M and radius R, with radius of gyration K, released from rest at the top of an inclined plane of angle , and allowed to roll DOWN without slipping.

Use g = 10 m/s², unless, otherwise stated.

Sample papers and previous-year board questions for this subject.