(C) Given: Radius $R = 0.2\, m$,Mass $M = 5\, kg$,Angular velocity $\omega = 2 + 6t$.First,find the angular acceleration $\alpha$ by differentiating $

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(C) Given: Radius $R = 0.2\, m$,Mass $M = 5\, kg$,Angular velocity $\omega = 2 + 6t$.First,find the angular acceleration $\alpha$ by differentiating $\omega$ with respect to time $t$:$\alpha = \frac{d\omega}{dt} = \frac{d}{dt}(2 + 6t) = 6\, rad/s^2$.The moment of inertia $I$ of a disc about its central axis is $I = \frac{1}{2}MR^2$.$I = \frac{1}{2} \times 5 \times (0.2)^2 = 0.5 \times 5 \times 0.04 = 0.1\, kg \cdot m^2$.The torque $\tau$ is given by $\tau = I\alpha = 0.1 \times 6 = 0.6\, N \cdot m$.Since $\tau = F \times R$,the tangential force $F$ is:$F = \frac{\tau}{R} = \frac{0.6}{0.2} = 3\, N$.

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

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$A$ homogeneous disc with a radius $0.2\, m$ and mass $5\, kg$ rotates around an axis passing through its centre. The angular velocity of the rotation of the disc as a function of time is given by the formula $\omega = 2 + 6t$. The tangential force applied to the rim of the disc is ........ $N.$

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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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An electric motor is started from rest to produce a torque. It acquires an angular acceleration given by $\alpha = 3t - t^2$. The angular acceleration becomes zero after $2 \ s$. Calculate the angular velocity after $6 \ s$.

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$A$ homogeneous disc with a radius $0.2\, m$ and mass $5\, kg$ rotates around an axis passing through its centre. The angular velocity of the rotation of the disc as a function of time is given by the formula $\omega = 2 + 6t$. The tangential force applied to the rim of the disc is ........ $N.$

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$A$ wheel is rotating at $600$ rpm about its axis of rotation. When the power is cut off, it comes to rest in half a minute. Its angular retardation expressed in rad/s$^2$ is (retardation is uniform).

$A$ circular disc rotating with frequency $f_0 = 1.3 \, rev/sec$ comes to a stop in $30 \, seconds$. The approximate angular acceleration is ....... $rad/sec^2$.

$A$ thin uniform stick of length $l$ and mass $m$ is held horizontally with its end $B$ hinged on the edge of a table. Point $A$ is suddenly released. The acceleration of the centre of mass of the stick at the time of release is:

An electric motor is started from rest to produce a torque. It acquires an angular acceleration given by $\alpha = 3t - t^2$. The angular acceleration becomes zero after $2 \ s$. Calculate the angular velocity after $6 \ s$.

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