(C) The torque $\tau$ applied to the flywheel is given by $\tau = F \times r$. Given $F = 10 \, N$ and $r = 0.2 \, m$,we have $\tau = 10 \times 0.2 =

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(C) The torque $\tau$ applied to the flywheel is given by $\tau = F \times r$. Given $F = 10 \, N$ and $r = 0.2 \, m$,we have $\tau = 10 \times 0.2 = 2 \, N \cdot m$. From the relation $\tau = I \alpha$,where $I = 0.4 \, kg \cdot m^2$ is the moment of inertia and $\alpha$ is the angular acceleration,we get $\alpha = \frac{\tau}{I} = \frac{2}{0.4} = 5 \, rad \cdot s^{-2}$. Assuming the flywheel starts from rest $(\omega_1 = 0)$,the angular velocity $\omega_2$ after time $t = 4 \, s$ is given by $\omega_2 = \omega_1 + \alpha t$. Substituting the values,$\omega_2 = 0 + (5 \times 4) = 20 \, rad \cdot s^{-1}$.

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

Medium

$A$ flywheel of moment of inertia $0.4 \, kg \, m^2$ and radius $0.2 \, m$ is free to rotate about a central axis. If a string is wrapped around it and it is pulled with a force of $10 \, N$,then the angular velocity after $4 \, s$ will be ......... $rad \, s^{-1}$.

A
$10$
B
$5$
C
$20$
D
$25$

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System of Particles and Rotational Motion

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Relation between Torque and Angular acceleration and it's Application

$A$ rod of length $50\,cm$ is pivoted at one end. It is raised such that it makes an angle of $30^o$ from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in $rad\,s^{-1}$) will be $(g = 10\,ms^{-2})$.

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$A$ wheel is rotating at a rate of $900$ revolutions per minute about its axis. When the power source is cut off,it comes to rest in $1$ minute. The angular retardation of the wheel in $rad/s^2$ is:

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$A$ mass of $10 \ kg$ is attached to one end of a massless rod and rotated in a circle of radius $30 \ cm$ with an angular velocity of $10 \ rad/s$. If the body is brought to rest in $10 \ s$ by applying a brake,the magnitude of the torque applied will be ...... $N-m$.

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$A$ rope of negligible mass is wound round a hollow cylinder of mass $3 \, kg$ and radius $40 \, cm$. If the rope is pulled with a force of $30 \, N$,then the angular acceleration produced in the cylinder is ........ $rad \, s^{-2}$.

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$A$ hollow sphere of mass $1 \,kg$ and radius $10 \,cm$ is free to rotate about its diameter. If a force of $30 \,N$ is applied tangentially to it,its angular acceleration is (in $rad/s^2$):

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$A$ flywheel of moment of inertia $0.4 \, kg \, m^2$ and radius $0.2 \, m$ is free to rotate about a central axis. If a string is wrapped around it and it is pulled with a force of $10 \, N$,then the angular velocity after $4 \, s$ will be ......... $rad \, s^{-1}$.

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$A$ rod of length $50\,cm$ is pivoted at one end. It is raised such that it makes an angle of $30^o$ from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in $rad\,s^{-1}$) will be $(g = 10\,ms^{-2})$.

$A$ wheel is rotating at a rate of $900$ revolutions per minute about its axis. When the power source is cut off,it comes to rest in $1$ minute. The angular retardation of the wheel in $rad/s^2$ is:

$A$ mass of $10 \ kg$ is attached to one end of a massless rod and rotated in a circle of radius $30 \ cm$ with an angular velocity of $10 \ rad/s$. If the body is brought to rest in $10 \ s$ by applying a brake,the magnitude of the torque applied will be ...... $N-m$.

$A$ rope of negligible mass is wound round a hollow cylinder of mass $3 \, kg$ and radius $40 \, cm$. If the rope is pulled with a force of $30 \, N$,then the angular acceleration produced in the cylinder is ........ $rad \, s^{-2}$.

$A$ hollow sphere of mass $1 \,kg$ and radius $10 \,cm$ is free to rotate about its diameter. If a force of $30 \,N$ is applied tangentially to it,its angular acceleration is (in $rad/s^2$):

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