Chapter 6: Systems of Particles and Rotational Motion Short Questions | physics Class 11 CBSE

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Chapter 6: Systems of Particles and Rotational Motion Short Questions | physics Class 11 CBSE | ByteNotes.in

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Question 1

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Define a rigid body and explain why no real body is truly rigid.

A rigid body is one for which the distances between all pairs of particles remain perfectly constant and unchanging even when forces are applied.
No real body is truly rigid because real bodies deform under the influence of forces; they may bend, twist, or vibrate to some extent.
However, when deformations are negligible — as in wheels, steel beams, planets — the body may be treated as rigid for practical analysis.

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Question 2

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State the condition for pure translational motion of a rigid body.

In pure translational motion, all particles of the rigid body have the same velocity at any given instant of time.
The body moves such that any line in the body remains parallel to its original direction throughout the motion.
A block sliding down a smooth inclined plane without rotating is a standard example of pure translational motion.

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Question 3

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What happens to the velocity of a particle lying exactly on the axis of rotation of a rotating rigid body?

For any particle on the axis of rotation, its perpendicular distance from the axis is r = 0.
Since linear velocity v = ωr, a particle on the axis has v = ω × 0 = 0, meaning it remains stationary.
This confirms that the axis is fixed in space — all particles on the fixed axis remain stationary while the rest of the body rotates around it.

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Question 4

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Write the formula for the position of the centre of mass of a two-particle system and explain each term.

The position of the CM is X = (m1x1 + m2x2)/(m1 + m2), where m1 and m2 are the masses and x1, x2 are the distances of the particles from the origin.
X can be interpreted as the mass-weighted mean of x1 and x2; particles of greater mass pull the CM closer to themselves.
When m1 = m2, the formula simplifies to X = (x1 + x2)/2, meaning the CM lies exactly at the midpoint between the two equal masses.

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Question 5

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Show that the centre of mass of a uniform thin rod coincides with its geometric centre.

Taking the geometric centre of the rod as the origin with the x-axis along the length, reflection symmetry applies: for every mass element dm at position +x, there is an equal element dm at −x.
The integral ∫x dm therefore sums equal and opposite contributions and equals zero.
Since ∫x dm = 0 implies X = 0, the CM is at the origin, which is the geometric centre of the rod.

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Question 6

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State what the equation MA = Fext tells us about the motion of the centre of mass of a system of particles.

The equation states that the total mass M of the system times the acceleration A of its CM equals the vector sum of all external forces Fext acting on the system.
It means the CM moves as if all the mass of the system is concentrated at that point and all external forces act at that point.
Internal forces between particles, which come in equal and opposite pairs by Newton's third law, do not appear in this equation and have no effect on the motion of the CM.

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Question 7

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A projectile explodes midway in air. Describe the subsequent motion of its centre of mass.

The forces causing the explosion are internal forces between the fragments; they contribute nothing to the motion of the CM.
The only external force acting on the system before and after the explosion is gravity, which remains unchanged.
Therefore the CM of the fragments continues along the same parabolic trajectory that the projectile would have followed had there been no explosion.

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Question 8

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State the law of conservation of linear momentum for a system of particles and the condition under which it holds.

If the total external force acting on a system of particles is zero, the total linear momentum P of the system remains constant.
This follows from dP/dt = Fext; when Fext = 0, dP/dt = 0, so P = constant.
Equivalently, the velocity of the CM remains constant, meaning the CM moves uniformly in a straight line when no net external force acts.

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Question 9

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Define the vector product of two vectors and state any two of its important properties.

The vector product (cross product) of vectors a and b is a vector c = a × b with magnitude ab sinθ, where θ is the angle between them, directed perpendicular to both by the right-hand rule.
Property 1: The vector product is anti-commutative — a × b = −b × a, so reversing the order reverses the direction of the resultant.
Property 2: The vector product of a vector with itself is zero — a × a = 0, since sin 0° = 0.

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Question 10

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Express the linear velocity of a particle of a rotating rigid body in terms of angular velocity using a vector relation.

The linear velocity of a particle at position r relative to a point on the axis of rotation is given by the vector equation v = ω × r.
Here ω is the angular velocity vector directed along the axis of rotation, and r is the position vector of the particle from the origin on the axis.
The magnitude is v = ωr⊥, where r⊥ is the perpendicular distance of the particle from the axis; the velocity is tangential to the circular path.

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Question 11

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Define angular acceleration and state its SI unit and dimensions.

Angular acceleration α is the time rate of change of angular velocity, defined as α = dω/dt.
For rotation about a fixed axis, the vector equation reduces to a scalar: α = dω/dt, with the direction along the fixed axis.
The SI unit of angular acceleration is rad s−2, and its dimensions are [T−2].

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Question 12

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Define torque and state the conditions under which torque due to a force is zero.

Torque is defined as τ = r × F; its magnitude is τ = rF sinθ where θ is the angle between the position vector r and force F, and its SI unit is N m.
Torque is zero if the magnitude of the force F is zero, meaning no force is applied.
Torque is also zero if the particle is at the origin (r = 0) or if the line of action of the force passes through the origin (θ = 0° or 180°).

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Question 13

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Define angular momentum of a particle. Write its SI unit and dimensional formula.

The angular momentum of a particle with linear momentum p at position r from the origin is defined as l = r × p; its magnitude is l = rp sinθ.
Angular momentum is the rotational analogue of linear momentum, sometimes also referred to as moment of (linear) momentum.
Its SI unit is joule-second (J s) or kg m² s−1, and its dimensional formula is [ML²T−1].

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Chapter sections

Chapter 6: Systems of Particles and Rotational Motion | Short Questions

Define a rigid body and explain why no real body is truly rigid.

State the condition for pure translational motion of a rigid body.

What happens to the velocity of a particle lying exactly on the axis of rotation of a rotating rigid body?

Write the formula for the position of the centre of mass of a two-particle system and explain each term.

Show that the centre of mass of a uniform thin rod coincides with its geometric centre.

State what the equation MA = Fext tells us about the motion of the centre of mass of a system of particles.

A projectile explodes midway in air. Describe the subsequent motion of its centre of mass.

State the law of conservation of linear momentum for a system of particles and the condition under which it holds.

Define the vector product of two vectors and state any two of its important properties.

Express the linear velocity of a particle of a rotating rigid body in terms of angular velocity using a vector relation.

Define angular acceleration and state its SI unit and dimensions.

Define torque and state the conditions under which torque due to a force is zero.

Define angular momentum of a particle. Write its SI unit and dimensional formula.

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