(C) For body $A$,$\theta_A = k_1 t^2$. Since it completes $1$ revolution ($2\pi$ radians) in $\sqrt{\pi} \ s$,we have $2\pi = k_1 (\sqrt{\pi})^2 = k_1

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(C) For body $A$,$\theta_A = k_1 t^2$. Since it completes $1$ revolution ($2\pi$ radians) in $\sqrt{\pi} \ s$,we have $2\pi = k_1 (\sqrt{\pi})^2 = k_1 \pi$,so $k_1 = 2$. Thus,$\theta_A = 2t^2$. The angular velocity is $\omega_A = \frac{d\theta_A}{dt} = 4t$. At $t = 5 \ s$,$\omega_A = 4(5) = 20 \ rad/s$.For body $B$,$\theta_B = k_2 t$. Since it completes half a revolution ($\pi$ radians) in $4\pi \ s$,we have $\pi = k_2 (4\pi)$,so $k_2 = 1/4$. Thus,$\theta_B = \frac{1}{4}t$. The angular velocity is $\omega_B = \frac{d\theta_B}{dt} = 1/4 \ rad/s$.The ratio $\omega_A : \omega_B = 20 : (1/4) = 80 : 1$.

Class 11 Physics 3-2.Motion in Plane Kinematics Circular Motion (Uniform Angular Accelaration)

Two bodies $A$ and $B$ rotate about an axis,such that the angle $\theta_A$ (in radians) covered by the first body is proportional to the square of time,and $\theta_B$ (in radians) covered by the second body varies linearly with time. At $t = 0$,$\theta_A = \theta_B = 0$. If $A$ completes its first revolution in $\sqrt{\pi} \ s$ and $B$ needs $4\pi \ s$ to complete half a revolution,then the ratio of their angular velocities $\omega_A : \omega_B$ at $t = 5 \ s$ is:

A
$4 : 1$
B
$20 : 1$
C
$80 : 1$
D
$20 : 4$

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3-2.Motion in Plane

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Kinematics Circular Motion (Uniform Angular Accelaration)

$A$ particle starting from rest moves along the circumference of a circle of radius $r$ with constant angular acceleration $\alpha$. The magnitude of the average velocity,in the time it completes a small angular displacement $\theta$,is:

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If the linear speed of a particle performing uniform circular motion is increased to $4$ times and its angular velocity is doubled,then the centripetal acceleration of the particle becomes .....

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$A$ car wheel is rotating at $1200$ revolutions per minute. On pressing the accelerator,it reaches $4500$ revolutions per minute in $10 \, s$. The angular acceleration of the wheel is:

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$A$ wheel which is initially at rest is subjected to a constant angular acceleration about its axis. It rotates through an angle of $15^{\circ}$ in time $t \ s$. The increase in angle through which it rotates in the next $2t \ s$ is (in $^{\circ}$)

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Is the tangential acceleration of a particle moving in a circular path always zero? Under what condition is it zero?

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