(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

$A$ wheel is at rest in a horizontal position. Its moment of inertia about the vertical axis passing through its centre is $I$. $A$ constant torque $\tau$ acts on it for $t$ seconds. The change in rotational kinetic energy is:

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$A$ flywheel gains a speed of $540\ r.p.m.$ in $6\ s$. Its angular acceleration will be

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Consider a particle of mass $m$ having linear momentum $\vec{p}$ at position $\vec{r}$ relative to the origin $O$. Let $\vec{L}$ be the angular momentum of the particle with respect to the origin. Which of the following equations correctly relate $\vec{r}, \vec{p}$ and $\vec{L}$?

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$A$ constant torque acting on a uniform circular wheel changes its angular momentum from $A_0$ to $4 A_0$ in $4$ seconds. The magnitude of this torque is ...........

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$A$ disc has mass $M$ and radius $R$. How much tangential force should be applied to the rim of the disc so as to rotate the disc with angular velocity $\omega$ in time $t$?

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$A$ wheel is at rest in a horizontal position. Its moment of inertia about the vertical axis passing through its centre is $I$. $A$ constant torque $\tau$ acts on it for $t$ seconds. The change in rotational kinetic energy is:

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