(A) Given: Radius $r = 1.5 \ m$,angular acceleration $\alpha = 10 \ rad/s^2$,initial angular speed $\omega_0 = (\frac{60}{\pi}) \ rpm$,time $t = 2.0 \

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(A) Given: Radius $r = 1.5 \ m$,angular acceleration $\alpha = 10 \ rad/s^2$,initial angular speed $\omega_0 = (\frac{60}{\pi}) \ rpm$,time $t = 2.0 \ s$.First,convert $\omega_0$ to $rad/s$:$\omega_0 = \frac{60}{\pi} \times \frac{2\pi}{60} = 2 \ rad/s$.Using the first equation of rotational motion,$\omega = \omega_0 + \alpha t$:$\omega = 2 + (10 \times 2) = 2 + 20 = 22 \ rad/s$.Using the second equation of rotational motion for angular displacement,$\theta = \omega_0 t + \frac{1}{2} \alpha t^2$:$\theta = (2 \times 2) + \frac{1}{2} \times 10 \times (2)^2 = 4 + (5 \times 4) = 4 + 20 = 24 \ rad$.

Class 11 Physics System of Particles and Rotational Motion Rotation Motion Basic, Motion of Connected Mass

Medium

$A$ wheel of radius $1.5 \ m$ rotates with a constant angular acceleration of $10 \ rad/s^2$. Its initial angular speed is $(\frac{60}{\pi}) \ rpm$. What will be its angular speed and angular displacement at $t = 2.0 \ s$?

A
$22 \ rad/s, 24 \ rad$
B
$20 \ rad/s, 20 \ rad$
C
$24 \ rad/s, 22 \ rad$
D
$18 \ rad/s, 26 \ rad$

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System of Particles and Rotational Motion

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Rotation Motion Basic, Motion of Connected Mass

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$A$ disc rotating about its axis from rest,acquires the angular speed $100 \, rev/s$ in $4 \, s$. The angle rotated by it during these four seconds (in radian) is ...... $\pi$.

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$A$ wheel of radius $1.5 \ m$ rotates with a constant angular acceleration of $10 \ rad/s^2$. Its initial angular speed is $(\frac{60}{\pi}) \ rpm$. What will be its angular speed and angular displacement at $t = 2.0 \ s$?

Similar Questions

$A$ truck is moving at a speed of $54 \ km/h$. The radius of its wheels is $50 \ cm$. If the wheels come to rest after $20$ rotations upon applying brakes,what is the linear distance covered by the truck during this time? What is the angular acceleration of the wheels?

In the given figure,a solid cylinder of mass $m_2$ and radius $R$ is suspended by a string wrapped around it,which passes over a fixed pulley of mass $m_1$ and radius $R$. If the linear acceleration of the solid cylinder is $a_2$ and there is no slipping,what is its angular acceleration $\alpha_2$?

In the figure shown,a mass $m$ is attached to a light string which is wrapped around a solid cylinder of mass $M$ and radius $R$. The system starts from rest at $t = 0$. If friction is negligible,what will be the angular velocity at time $t$?

$A$ string is wrapped around a cylinder of radius $r$ and moment of inertia $I$. $A$ mass $m$ is attached to one end of the string. The cylinder can rotate freely about its horizontal axis. If the mass $m$ is released from rest at a height $h$,what will be its velocity?

$A$ disc rotating about its axis from rest,acquires the angular speed $100 \, rev/s$ in $4 \, s$. The angle rotated by it during these four seconds (in radian) is ...... $\pi$.

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