Ch 5Motion of System of Particles and Rigid Bodies — Class 11 Physics, concept-first.

Every unit until now treated bulk bodies as if they were single point objects, ignoring size and shape entirely.

Not every particle of a moving rigid body follows the same path. Depending on exactly how the body moves — purely sliding, purely spinning, or some mixture of both — different particles of the body ca…

Consider a bulk object, such as a bat, thrown spinning through the air at some angle. Every part of the bat is undergoing a complicated combined motion, tumbling end over end as it also arcs through t…

To locate the center of mass of a collection of discrete point masses , the first step is to choose an origin and a coordinate system.

Applying the general center-of-mass formula to the simplest possible case — just two point masses and on the X-axis, at positions and — gives three equivalent, but differently convenient, expressions…

The discrete-sum formulas of §5.1.3 assumed the mass was concentrated at a handful of distinct points.

Since the center of mass has a well-defined position at every instant, it also has a well-defined velocity and acceleration, obtained simply by differentiating its position with respect to time once a…

When a net force acts on a body that is free to move, it simply produces linear motion in the direction of the force.

Torque is defined as the moment of an externally applied force about a chosen point or axis of rotation.

The idea of torque about a single point extends naturally to the more physically relevant idea of torque about a fixed axis, which is what actually governs a rigid body constrained to rotate about a l…

Consider a rigid body constrained to rotate about a fixed axis, and within it a single point mass executing circular motion about that axis at distance .

Angular momentum is the rotational counterpart of linear momentum, and — importantly — it is a well-defined quantity for any moving particle, not only for particles undergoing circular or rotational m…

Now specialise angular momentum to the case that gives it its most familiar, everyday meaning: a point mass that is part of a rigid body, executing genuine circular motion about a fixed axis at distan…

Having established for a rigid body's angular momentum and for the torque acting on it, these two results can be directly combined.

It is tempting to think that a body lying perfectly still on a table experiences no force at all — but this is not quite right.

Translational equilibrium. When a body's linear momentum stays constant, the net force acting on it is zero: meaning the vector sum of every individual force acting on the body, , is exactly zero.

Consider a thin, uniform rod , whose center of mass sits at its midpoint . Now apply two forces at the two ends and of the rod, both perpendicular to the rod, equal in magnitude, but pointing in oppos…

Consider a light rod (of negligible mass) pivoted at a single point along its length, with two parallel forces and acting at its two ends, at distances and respectively from the pivot, along with the…

Every rigid body is, at bottom, a collection of a great many point masses, and each of these individual point masses experiences its own small gravitational pull towards the center of the Earth.

Consider a cyclist negotiating a level (unbanked) circular road of radius at speed . Treating the cyclist and cycle together as a single system of mass with center of gravity , this system travels in…

Just as mass measures a body's inherent resistance to any change in its state of linear motion (its inertia), moment of inertia measures a body's resistance to a change in its state of rotational moti…

Consider a uniform rod of mass and length , and find its moment of inertia about the axis passing through its own center of mass, perpendicular to the rod (Figure 5.21).

Consider a uniform ring of mass and radius , and find its moment of inertia about an axis through its center, perpendicular to the plane of the ring.

Consider a solid disc of mass and radius , and find its moment of inertia about an axis through its center, perpendicular to the plane of the disc.

For a body of regular shape with uniform mass distribution, the moment of inertia formula naturally involves the body's total mass together with geometric quantities such as its radius, length or brea…

Because moment of inertia depends on the axis of rotation and the body's orientation relative to it, the very same body has a different moment of inertia about every different axis one might choose.

The two integration-based derivations of §5.4.1–§5.4.3 (rod, ring, disc), together with the two theorems of §5.4.5, are enough in principle to derive the moment of inertia of any standard regularly-sh…

The relations connecting torque, angular acceleration, angular momentum, angular velocity and moment of inertia were already developed in §5.2.

A rigid body with a nonzero net external torque acting about its axis of rotation experiences an angular acceleration about that same axis, related to the torque by the scalar equation where is the bo…

When no external torque acts on a rotating rigid body (or system of particles), its net angular momentum stays exactly constant over time — this is the law of conservation of angular momentum, already…

Consider a rigid body rotating about a fixed axis perpendicular to the page, and a point on the body acted on by a tangential force .

Consider a rigid body rotating with angular velocity about a fixed axis. Every particle of the body shares this same angular velocity , but has its own distinct tangential (linear) velocity, depending…

Power delivered is simply the rate at which work is done. Differentiating the expression for work done by a torque, , with respect to time: Since , the angular velocity, this gives the instantaneous p…

Many of the rotational quantities developed across §5.2 and §5.5 have expressions that are structurally identical to their translational-motion counterparts, differing only in which symbols are used.

Rolling motion — a ring, disc, sphere or wheel rolling along a surface — is among the most commonly observed forms of motion in everyday life, from a rolling ball to every wheeled vehicle on the road.…

How translation and rotation combine in rolling. If a rolling object has radius , then in one complete rotation, the center of mass is displaced by exactly the object's own circumference, .

A round object rolling on any surface with a nonzero coefficient of friction () always tends towards pure rolling — the friction responsible for enabling and maintaining this is called rolling frictio…

Since pure rolling is a combination of translational and rotational motion happening simultaneously, its total kinetic energy is simply the sum of a translational part and a rotational part: If the ro…

Consider a round object of mass and radius rolling without slipping down an incline of angle . Two forces act on it along the direction of the incline: the driving component of gravity, , and an oppos…

This unit's key results, gathered together:

The unit's concept map traces the logical spine of the whole chapter. It begins with the rigid body idealisation and its center of mass — the single point standing in for the whole body's translationa…

This closing exercise set tests every idea developed across the unit, in five question formats:

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