(A) Given: Radius $r = 0.4 \ m$,Angular acceleration $\alpha = 8 \ rad \ s^{-2}$,Mass $m = 4 \ kg$,Acceleration due to gravity $g = 10 \ ms^{-2}$.The

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(A) Given: Radius $r = 0.4 \ m$,Angular acceleration $\alpha = 8 \ rad \ s^{-2}$,Mass $m = 4 \ kg$,Acceleration due to gravity $g = 10 \ ms^{-2}$.The torque $\tau$ produced by the weight is given by $\tau = mgr$.Also,the torque is related to the moment of inertia $I$ and angular acceleration $\alpha$ by $\tau = I\alpha$.Equating the two expressions for torque:$I\alpha = mgr$$I \times 8 = 4 \times 10 \times 0.4$$I \times 8 = 16$$I = \frac{16}{8} = 2 \ kg \ m^2$.

Class 11 Physics System of Particles and Rotational Motion Relation between Torque and Angular acceleration and it's Application

Medium

$A$ wheel of radius $0.4 \ m$ can rotate freely about its axis as shown in the figure. $A$ string is wrapped around its circumference,and a weight of $4 \ kg$ is suspended from it. Due to the torque,an angular acceleration of $8 \ rad \ s^{-2}$ is produced. The moment of inertia of the wheel is = $...... \ kg \ m^2$ $(g = 10 \ ms^{-2})$

A
$2$
B
$1$
C
$4$
D
$8$

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Class 11

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System of Particles and Rotational Motion

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Relation between Torque and Angular acceleration and it's Application

$A$ rope of negligible mass is wound round a hollow cylinder of mass $3\; kg$ and radius $40\; cm$. What is the angular acceleration of the cylinder if the rope is pulled with a force of $30\; N$? What is the linear acceleration of the rope? Assume that there is no slipping.

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$A$ rectangular solid rod of length $0.3\, m$ is held horizontally,with one of its sides on the edge of a platform of height $5\, m$. When released,it slips off the table in a very short time $\Delta t = 0.01\, s$,remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to:

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The grinding stone of a flour mill is rotating at $600 \, rad/s$. For this, a power of $1.2 \, kW$ is used. The effective torque on the stone in $N-m$ will be:

Easy

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$A$ uniform metre stick of mass $M$ and length $L = 1 \ m$ is hinged at one end and supported in a horizontal direction by a string attached to the other end. What should be the initial angular acceleration of the free end of the stick if the string is cut? (in $rad/s^2$)

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$A$ massless rod of length $2l$ has equal point masses $m$ attached to its two ends as shown in the figure. The rod is rotating about an axis passing through its centre and making an angle $\alpha$ with the axis. The magnitude of the rate of change of angular momentum of the rod,i.e.,$\left|\frac{dL}{dt}\right|$,is equal to:

DifficultAIIMS 2015

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$A$ rope of negligible mass is wound round a hollow cylinder of mass $3\; kg$ and radius $40\; cm$. What is the angular acceleration of the cylinder if the rope is pulled with a force of $30\; N$? What is the linear acceleration of the rope? Assume that there is no slipping.

The grinding stone of a flour mill is rotating at $600 \, rad/s$. For this, a power of $1.2 \, kW$ is used. The effective torque on the stone in $N-m$ will be:

$A$ uniform metre stick of mass $M$ and length $L = 1 \ m$ is hinged at one end and supported in a horizontal direction by a string attached to the other end. What should be the initial angular acceleration of the free end of the stick if the string is cut? (in $rad/s^2$)

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