(A) In the case of pure rolling,the bottommost point $O$ of the disc is the instantaneous center of rotation $(ICR)$,where the velocity is zero.The ve

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(A) In the case of pure rolling,the bottommost point $O$ of the disc is the instantaneous center of rotation $(ICR)$,where the velocity is zero.The velocity of any point on the disc is given by $V = r \omega$,where $r$ is the distance of the point from the instantaneous center $O$ and $\omega$ is the angular velocity of the disc.From the geometry of the disc,the distances of points $Q, C,$ and $P$ from the instantaneous center $O$ satisfy the relation $r_Q > r_C > r_P$.Since $V = r \omega$ and $\omega$ is constant for all points on the disc,it follows that $V_Q > V_C > V_P$.

Class 11 Physics System of Particles and Rotational Motion Toppling and Instantaneous Axis of Rotation

Medium

$A$ disc is rolling (without slipping) on a horizontal surface. $C$ is its center and $Q$ and $P$ are two points on the disc such that $Q$ is further from the contact point $O$ than $C$,and $P$ is closer to the contact point $O$ than $C$. Let $V_P, V_Q$ and $V_C$ be the magnitudes of the velocities of points $P, Q$ and $C$ respectively,then:

A
$V_Q > V_C > V_P$
B
$V_Q < V_C < V_P$
C
$V_Q = V_P, V_C = \frac{V_P + V_Q}{2}$
D
$V_Q < V_C > V_P$

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System of Particles and Rotational Motion

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Toppling and Instantaneous Axis of Rotation

$A$ cube with sides of length $2a$ and mass $M$ is moving with an initial speed $v_0$ along a frictionless table. When the cube reaches the end of the table it is caught abruptly by a short lip and begins to rotate. The minimum speed $v_0$ such that the cube falls off the table is

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The instantaneous velocity of point $B$ of a rod of length $0.5 \ m$ is $3 \ m/s$ at an angle of $30^{\circ}$ with the rod as shown. Find the angular velocity of the rod such that the velocity of end $A$ is minimum.

DifficultAP EAMCET 2005

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$A$ ladder of length $L$ is slipping with its ends against a vertical wall and a horizontal floor. At a certain moment,the speed of the end in contact with the horizontal floor is $v$ and the ladder makes an angle $\alpha = 30^o$ with the horizontal. Then the speed of the ladder's center must be

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$A$ disc rolls on a horizontal surface (without slipping). $C$ is the center and $Q$ and $P$ are two points at the same distance from $C$. Let $v_P$,$v_Q$,and $v_C$ be the magnitudes of the velocities of points $P$,$Q$,and $C$ respectively. Then:

Medium

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$A$ uniform cube of side '$a$' and mass '$m$' rests on a rough horizontal surface. $A$ horizontal force $F$ is applied normal to one of the faces at a point that is directly above the centre of the face,at a height $\frac{3a}{4}$ above the base. The minimum value of $F$ for which the cube begins to topple about the edge is (Assume that the cube does not slide).

Medium

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$A$ cube with sides of length $2a$ and mass $M$ is moving with an initial speed $v_0$ along a frictionless table. When the cube reaches the end of the table it is caught abruptly by a short lip and begins to rotate. The minimum speed $v_0$ such that the cube falls off the table is

The instantaneous velocity of point $B$ of a rod of length $0.5 \ m$ is $3 \ m/s$ at an angle of $30^{\circ}$ with the rod as shown. Find the angular velocity of the rod such that the velocity of end $A$ is minimum.

$A$ ladder of length $L$ is slipping with its ends against a vertical wall and a horizontal floor. At a certain moment,the speed of the end in contact with the horizontal floor is $v$ and the ladder makes an angle $\alpha = 30^o$ with the horizontal. Then the speed of the ladder's center must be

$A$ disc rolls on a horizontal surface (without slipping). $C$ is the center and $Q$ and $P$ are two points at the same distance from $C$. Let $v_P$,$v_Q$,and $v_C$ be the magnitudes of the velocities of points $P$,$Q$,and $C$ respectively. Then:

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