(D) Given:Moment of inertia $I = 0.20\, kg-m^2$Radius $r = 20\, cm = 0.2\, m$Force $F = 20\, N$Time $t = 5\, s$Initial angular velocity $\omega_0 = 0$

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(D) Given:Moment of inertia $I = 0.20\, kg-m^2$Radius $r = 20\, cm = 0.2\, m$Force $F = 20\, N$Time $t = 5\, s$Initial angular velocity $\omega_0 = 0$The torque applied to the wheel is $\tau = r \times F = 0.2\, m \times 20\, N = 4\, N-m$.Using the relation $\tau = I \alpha$,the angular acceleration is $\alpha = \frac{\tau}{I} = \frac{4}{0.20} = 20\, rad/s^2$.Using the equation of motion $\omega = \omega_0 + \alpha t$:$\omega = 0 + (20)(5) = 100\, rad/s$.

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

Medium

$A$ string is wrapped around the rim of a wheel of moment of inertia $0.20\, kg-m^2$ and radius $20\, cm$. The wheel is free to rotate about its axis and initially the wheel is at rest. The string is now pulled by a force of $20\, N$. The angular velocity of the wheel after $5\, s$ will be ....... $rad/s$.

A
$90$
B
$70$
C
$95$
D
$100$

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System of Particles and Rotational Motion

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Relation between Torque and Angular acceleration and it's Application

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

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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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$A$ constant torque is applied to a wheel undergoing uniform circular motion,causing its angular momentum to change from $A_0$ to $4A_0$ in $4 \ s$. The magnitude of this torque is .......

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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:

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

$A$ 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 ...... $N-m$.

$A$ constant torque is applied to a wheel undergoing uniform circular motion,causing its angular momentum to change from $A_0$ to $4A_0$ in $4 \ s$. The magnitude of this torque is .......

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:

$A$ 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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