(B) The torque $\tau$ applied by the force $F$ at a distance $r$ from the axis is given by $\tau = F \times r$.Substituting the values, $\tau = 25 \,N

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(B) The torque $\tau$ applied by the force $F$ at a distance $r$ from the axis is given by $\tau = F \times r$.Substituting the values, $\tau = 25 \,N \times 0.4 \,m = 10 \,Nm$.The moment of inertia $I$ of a solid cylinder about its own axis is $I = \frac{1}{2} M R^2$.Substituting the values, $I = \frac{1}{2} \times 1 \,kg \times (0.4 \,m)^2 = 0.5 \times 0.16 = 0.08 \,kg \cdot m^2$.Using the relation $\tau = I \alpha$, the angular acceleration $\alpha$ is $\alpha = \frac{\tau}{I}$.$\alpha = \frac{10 \,Nm}{0.08 \,kg \cdot m^2} = 125 \,rad/s^2$.

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

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$A$ rope is wound around a solid cylinder of mass $1 \,kg$ and radius $0.4 \,m$. What is the angular acceleration of the cylinder, if the rope is pulled with a force of $25 \,N$? (The cylinder is rotating about its own axis.)

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A
$50 \,rad/s^2$
B
$125 \,rad/s^2$
C
$10 \,rad/s^2$
D
$1 \,rad/s^2$

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System of Particles and Rotational Motion

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Relation between Torque and Angular acceleration and it's Application

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At time $t = 0$,a $2\, kg$ particle has position vector $\vec{r} = (4\hat{i} - 2\hat{j})\, m$ relative to the origin. Its velocity is given by $\vec{v} = 2t^2\hat{i}\, m/s$. The torque acting on the particle about the origin at $t = 2\, s$ is ........ $\hat{k}\, N\cdot m$.

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Define angular acceleration.

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What is the value of the torque acting on an object moving in a circular path with a constant angular speed? Why?

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$A$ uniform disc of mass $5\,g$ and radius $1\,cm$ is fixed to a thin stick $AB$ of negligible mass as shown in the figure. The system is initially at rest. The constant torque,that will make the system rotate about $AB$ at $25$ rotations per second in $5\,s$,is close to:

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$A$ disc of radius $0.4 \,m$ and mass $1 \,kg$ rotates about an axis passing through its center and perpendicular to its plane. The angular acceleration of the disc is $10 \,rad/s^2$. The tangential force applied to the rim of the disc is (in $\,N$)

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$A$ rope is wound around a solid cylinder of mass $1 \,kg$ and radius $0.4 \,m$. What is the angular acceleration of the cylinder, if the rope is pulled with a force of $25 \,N$? (The cylinder is rotating about its own axis.)

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At time $t = 0$,a $2\, kg$ particle has position vector $\vec{r} = (4\hat{i} - 2\hat{j})\, m$ relative to the origin. Its velocity is given by $\vec{v} = 2t^2\hat{i}\, m/s$. The torque acting on the particle about the origin at $t = 2\, s$ is ........ $\hat{k}\, N\cdot m$.

Define angular acceleration.

What is the value of the torque acting on an object moving in a circular path with a constant angular speed? Why?

$A$ uniform disc of mass $5\,g$ and radius $1\,cm$ is fixed to a thin stick $AB$ of negligible mass as shown in the figure. The system is initially at rest. The constant torque,that will make the system rotate about $AB$ at $25$ rotations per second in $5\,s$,is close to:

$A$ disc of radius $0.4 \,m$ and mass $1 \,kg$ rotates about an axis passing through its center and perpendicular to its plane. The angular acceleration of the disc is $10 \,rad/s^2$. The tangential force applied to the rim of the disc is (in $\,N$)

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