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CBSE - Class 11 > Physics > System of Particles and Rotational Motion Worksheets

Free CBSE - Class 11 Physics - System of Particles and Rotational Motion worksheets

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1.
Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass : (a) Show $p_i = p'_i + m_i V$ where $p_i$ is the momentum of the ith particle (of mass $m_i$) and $p'_i = m_i v'_i$. Note $v'_i$ is the velocity of the ith particle relative to the centre of mass. Also, prove using the definition of the centre of mass $\sum p'_i = 0$.
2.
Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass : (b) Show $K = K' + \frac{MV^2}{2}$ where $K$ is the total kinetic energy of the system of particles, $K'$ is the total kinetic energy of the system when the particle velocities are taken with respect to the centre of mass and $\frac{MV^2}{2}$ is the kinetic energy of the translation of the system as a whole (i.e. of the centre of mass motion of the system). The result has been used in Sec. 7.14.
3.
Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass : (c) Show $L = L' + R \times MV$ where $L' = \sum r'_i \times p'_i$ is the angular momentum of the system about the centre of mass with velocities taken relative to the centre of mass. Remember $r'_i = r_i - R$; rest of the notation is the standard notation used in the chapter. Note $L'$ and $M \times R V$ can be said to be angular momenta, respectively, about and of the centre of mass of the system of particles.
4.
Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass : (d) Show $\frac{d L'}{dt} = \sum r'_i \times \frac{dp'_i}{dt}$ Further, show that $\frac{d L'}{dt} = \tau'_{ext}$ where $\tau'_{ext}$ is the sum of all external torques acting on the system about the centre of mass. (Hint : Use the definition of centre of mass and third law of motion. Assume the internal forces between any two particles act along the line joining the particles.)
5.
(b) Prove the theorem of parallel axes. (Hint : If the centre of mass of a system of $n$ particles is chosen to be the origin $\sum m_i r_i = 0$).
6.

Explain why friction is necessary to make the disc in Fig. 7.41 roll in the direction indicated. (a) Give the direction of frictional force at B, and the sense of frictional torque, before perfect rolling begins.

7.

Explain why friction is necessary to make the disc in Fig. 7.41 roll in the direction indicated. (b) What is the force of friction after perfect rolling begins ?

8.
A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination $30^o$. The co-efficient of static friction $\mu_s = 0.25$. (a) How much is the force of friction acting on the cylinder ?
9.
A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination $30^o$. The co-efficient of static friction $\mu_s = 0.25$. (b) What is the work done against friction during rolling ?
10.
A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination $30^o$. The co-efficient of static friction $\mu_s = 0.25$. (c) If the inclination $\theta$ of the plane is increased, at what value of $\theta$ does the cylinder begin to skid, and not roll perfectly ?
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Chapters in CBSE - Class 11 Physics

Physical World Worksheet Units and Measurements Worksheet Motion in a Straight Line Worksheet Laws of Motion Worksheet Work Worksheet Gravitation Worksheet Mechanical Properties of Solids Worksheet Thermal Properties of Matter Worksheet Thermodynamics Worksheet Kinetic Theory Worksheet Oscillations Worksheet Waves Worksheet Motion in a Plane Worksheet Mechanical Properties of Fluids Worksheet

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