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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View Solution$A$ body of mass $1 \,kg$ is suspended by a weightless string which passes over a pulley of mass $2 \,kg$ as shown in the figure. The mass is released from a height of $1.6 \,m$ from the ground. With what velocity does it strike the ground?
DifficultKCET 2024
View SolutionIn the case of rotational dynamics,which one of the following statements is correct?
$[\vec{\omega} = \text{angular velocity}, \vec{v} = \text{linear velocity}, \vec{r} = \text{radius vector}, \vec{\alpha} = \text{angular acceleration}, \vec{a} = \text{linear acceleration}, \vec{L} = \text{angular momentum}, \vec{p} = \text{linear momentum}, \vec{\tau} = \text{torque}, \vec{f} = \text{force}]$
$[\vec{\omega} = \text{angular velocity}, \vec{v} = \text{linear velocity}, \vec{r} = \text{radius vector}, \vec{\alpha} = \text{angular acceleration}, \vec{a} = \text{linear acceleration}, \vec{L} = \text{angular momentum}, \vec{p} = \text{linear momentum}, \vec{\tau} = \text{torque}, \vec{f} = \text{force}]$
$Assertion :$ $A$ hollow shaft is found to be stronger than a solid shaft made of the same material and having the same mass per unit length.
$Reason :$ The torque required to produce a given twist in a hollow cylinder is greater than that required to twist a solid cylinder of the same length and material.
$Reason :$ The torque required to produce a given twist in a hollow cylinder is greater than that required to twist a solid cylinder of the same length and material.
MediumAIIMS 2016
View SolutionState the equivalent physical quantities in linear motion corresponding to the moment of inertia and torque in rotational motion.
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