(B) Since a frictional force acts at the point of contact with the ground,the total kinetic energy will not be conserved.However,the torque of this fr

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Angular momentum about the point of contact with the surface is conserved.

(B) Since a frictional force acts at the point of contact with the ground,the total kinetic energy will not be conserved.However,the torque of this frictional force about the point of contact is zero because the force acts exactly at that point.Therefore,the angular momentum of the sphere about the point of contact remains constant.Mathematically,$\vec{\tau} = \frac{d\vec{L}}{dt}$. If $\vec{\tau} = 0$,then $\vec{L} = \text{constant}$.

Class 11 Physics System of Particles and Rotational Motion Rolling motion on horizontal Surface

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$A$ solid homogeneous sphere is rolling with sliding on a horizontal rough surface. For this type of motion of the sphere:

A
Total kinetic energy is conserved.
B
Angular momentum about the point of contact with the surface is conserved.
C
Only rotational kinetic energy about the center of mass is conserved.
D
Angular momentum about the center of mass is conserved.

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System of Particles and Rotational Motion

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Rolling motion on horizontal Surface

$A$ circular ring of mass $10 \text{ kg}$ rolls along a horizontal floor. The center of mass of the ring has a speed of $1.5 \text{ m/s}$. The work required to stop the ring is: (in $\text{ J}$)

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Explain why friction is necessary to make the disc in the figure roll in the direction indicated.
$(a)$ Give the direction of frictional force at $B$,and the sense of frictional torque,before perfect rolling begins.
$(b)$ What is the force of friction after perfect rolling begins?

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$A$ symmetrical body of mass $M$ and radius $R$ is rolling without slipping on a horizontal surface with linear speed $v$. Then its angular speed is

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For a rolling body,the velocities of points $P_1$ and $P_2$ are ${\vec v_1}$ and ${\vec v_2}$,respectively. Which of the following is correct?

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Consider a cylinder of mass $M$ resting on a rough horizontal rug that is pulled out from under it with acceleration $a$ perpendicular to the axis of the cylinder. What is the friction force $F_{friction}$ at point $P$? It is assumed that the cylinder does not slip.

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$A$ solid homogeneous sphere is rolling with sliding on a horizontal rough surface. For this type of motion of the sphere:

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$A$ circular ring of mass $10 \text{ kg}$ rolls along a horizontal floor. The center of mass of the ring has a speed of $1.5 \text{ m/s}$. The work required to stop the ring is: (in $\text{ J}$)

Explain why friction is necessary to make the disc in the figure roll in the direction indicated.$(a)$ Give the direction of frictional force at $B$,and the sense of frictional torque,before perfect rolling begins.$(b)$ What is the force of friction after perfect rolling begins?

$A$ symmetrical body of mass $M$ and radius $R$ is rolling without slipping on a horizontal surface with linear speed $v$. Then its angular speed is

For a rolling body,the velocities of points $P_1$ and $P_2$ are ${\vec v_1}$ and ${\vec v_2}$,respectively. Which of the following is correct?

Consider a cylinder of mass $M$ resting on a rough horizontal rug that is pulled out from under it with acceleration $a$ perpendicular to the axis of the cylinder. What is the friction force $F_{friction}$ at point $P$? It is assumed that the cylinder does not slip.

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Explain why friction is necessary to make the disc in the figure roll in the direction indicated.
$(a)$ Give the direction of frictional force at $B$,and the sense of frictional torque,before perfect rolling begins.
$(b)$ What is the force of friction after perfect rolling begins?