Class 11PhysicsSystem of Particles and Rotational MotionMix Example - System of Particles and Rotational Motion
MediumState whether the following statements are True or False:
$(1)$ Angular position $\theta$ is a scalar,while angular displacement $\Delta \theta$ is a vector.
$(2)$ The relation between linear velocity $\vec{v}$ and angular velocity $\vec{\omega}$ for a particle in rotational motion is given by $\vec{v} = \vec{r} \times \vec{\omega}$.
$(3)$ The moment of inertia of a rigid body is constant.
$(4)$ The moment of momentum is called angular momentum.
$(1)$ Angular position $\theta$ is a scalar,while angular displacement $\Delta \theta$ is a vector.
$(2)$ The relation between linear velocity $\vec{v}$ and angular velocity $\vec{\omega}$ for a particle in rotational motion is given by $\vec{v} = \vec{r} \times \vec{\omega}$.
$(3)$ The moment of inertia of a rigid body is constant.
$(4)$ The moment of momentum is called angular momentum.
(A) $(1)$ True. Angular displacement for small angles is treated as a vector.
$(2)$ False. The correct relation is $\vec{v} = \vec{\omega} \times \vec{r}$.
$(3)$ False. The moment of inertia depends on the axis of rotation and the distribution of mass relative to that axis.
$(4)$ True. Angular momentum is defined as the moment of linear momentum,$\vec{L} = \vec{r} \times \vec{p}$.
$(2)$ False. The correct relation is $\vec{v} = \vec{\omega} \times \vec{r}$.
$(3)$ False. The moment of inertia depends on the axis of rotation and the distribution of mass relative to that axis.
$(4)$ True. Angular momentum is defined as the moment of linear momentum,$\vec{L} = \vec{r} \times \vec{p}$.
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