(D) The angular displacement $\theta$ for an object starting from rest with constant angular acceleration $\alpha$ is given by $\theta = \frac{1}{2} \

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(D) The angular displacement $\theta$ for an object starting from rest with constant angular acceleration $\alpha$ is given by $\theta = \frac{1}{2} \alpha t^2$.For the first $2 \ s$ $(t_1 = 2 \ s)$: $\theta_1 = \frac{1}{2} \alpha (2)^2 = 2\alpha$.For the total time of $4 \ s$ $(t_2 = 2 + 2 = 4 \ s)$: $\theta_{total} = \frac{1}{2} \alpha (4)^2 = 8\alpha$.The angle rotated in the next $2 \ s$ is $\theta_2 = \theta_{total} - \theta_1 = 8\alpha - 2\alpha = 6\alpha$.Therefore,the ratio $\theta_1 : \theta_2 = 2\alpha : 6\alpha = 1 : 3$.

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

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$A$ wheel initially at rest,begins to rotate about its axis with constant angular acceleration. If it rotates through an angle $\theta_1$ in first $2 \ s$ and a further angle $\theta_2$ in the next $2 \ s$,the ratio $\theta_1 : \theta_2$ is

MHT CET 2025 All MHT CET

A
$1: 6$
B
$6: 1$
C
$3: 1$
D
$1: 3$

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$A$ wheel initially at rest,begins to rotate about its axis with constant angular acceleration. If it rotates through an angle $\theta_1$ in first $2 \ s$ and a further angle $\theta_2$ in the next $2 \ s$,the ratio $\theta_1 : \theta_2$ is

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If the position vector of a particle is $\vec{r} = (3\hat{i} + 4\hat{j}) \text{ m}$ and its angular velocity is $\vec{\omega} = (\hat{j} + 2\hat{k}) \text{ rad/s}$, then its linear velocity $\vec{v}$ is (in $\text{m/s}$):

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