Class 11PhysicsSystem of Particles and Rotational MotionMix Example - System of Particles and Rotational Motion
MediumFill in the blanks:
$(1)$ In rotational motion,the role played by ............ is analogous to the role played by mass in linear motion.
$(2)$ For a rigid body in rotational motion,if a particle at a distance of $10 \ cm$ from the fixed axis of rotation has an angular velocity of $10 \ rad/s$,then the linear velocity of a particle at a distance of $5 \ cm$ from the axis of rotation is ............
$(3)$ The $SI$ unit $J \cdot s^{-2}$ is the unit of the physical quantity ............
$(4)$ The condition for a body to roll without slipping down an inclined plane with friction is ............
$(1)$ In rotational motion,the role played by ............ is analogous to the role played by mass in linear motion.
$(2)$ For a rigid body in rotational motion,if a particle at a distance of $10 \ cm$ from the fixed axis of rotation has an angular velocity of $10 \ rad/s$,then the linear velocity of a particle at a distance of $5 \ cm$ from the axis of rotation is ............
$(3)$ The $SI$ unit $J \cdot s^{-2}$ is the unit of the physical quantity ............
$(4)$ The condition for a body to roll without slipping down an inclined plane with friction is ............
(N/A) $(1)$ Moment of inertia.
$(2)$ Given: $\omega = 10 \ rad/s$,$r = 5 \ cm$.
Using the relation $v = \omega r$,we get $v = 10 \times 5 = 50 \ cm/s$.
$(3)$ Torque $(\tau)$. Since $\tau = I\alpha$,the unit is $kg \cdot m^2 \cdot rad/s^2 = (kg \cdot m^2) \cdot s^{-2} = J \cdot s^{-2}$.
$(4)$ The condition for rolling without slipping on an inclined plane is $\mu_s \geq \left( \frac{\tan \theta}{1 + \frac{R^2}{K^2}} \right)$.
$(2)$ Given: $\omega = 10 \ rad/s$,$r = 5 \ cm$.
Using the relation $v = \omega r$,we get $v = 10 \times 5 = 50 \ cm/s$.
$(3)$ Torque $(\tau)$. Since $\tau = I\alpha$,the unit is $kg \cdot m^2 \cdot rad/s^2 = (kg \cdot m^2) \cdot s^{-2} = J \cdot s^{-2}$.
$(4)$ The condition for rolling without slipping on an inclined plane is $\mu_s \geq \left( \frac{\tan \theta}{1 + \frac{R^2}{K^2}} \right)$.
Explore More
Similar Questions
$A$ solid metallic sphere of radius '$R$' having moment of inertia '$I$' about its diameter is melted and recast into a solid disc of radius '$r$' of uniform thickness. The moment of inertia of the disc about an axis passing through its edge and perpendicular to its plane is also equal to '$I$'. The ratio $\frac{r}{R}$ is
$A$ ring of radius $R$ rolls without sliding with a constant velocity $u$. The radius of curvature of the path followed by any particle of the ring at the highest point of its path will be
Difficult
View SolutionFour particles each of mass $m$ are lying symmetrically on the rim of a disc of mass $M$ and radius $R$. The moment of inertia of the system about an axis passing through one of the particles and perpendicular to the plane of the disc is:
$A$ particle executes uniform circular motion with angular momentum $L$. Its rotational kinetic energy becomes half,when the angular frequency is doubled. Its new angular momentum is
$A$ ring and a disc have the same mass and the same radius. The ratio of the moment of inertia of a ring about a tangent in its plane to that of the disc about its diameter is: (in $: 1$)
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo