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
$A$ plank with a uniform sphere placed on it rests on a smooth horizontal plane. The plank is pulled to the right by a constant force $F$. If the sphere does not slip over the plank,which of the following statements is incorrect?
Difficult
View Solution$A$ thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of:
MediumAIEEE 2009
View SolutionDuring a test of a jet engine,its compressor rotates according to the graph shown. The total number of revolutions completed by the compressor during the test is:
Difficult
View Solution$A$ solid sphere is in purely rotational motion about its diameter. The ratio of its angular momentum $(L)$ and kinetic energy $(K)$ is $\frac{\pi}{22}$. Find the angular velocity $(\omega)$ of the sphere. (Take $\pi = \frac{22}{7}$) (in $rad/s$)
$A$ body with a moment of inertia of $3\ kg\cdot m^2$ rotating with an angular velocity of $2\ rad/s$ has the same kinetic energy as a mass of $12\ kg$ moving with a velocity of .......... $m/s$.
Medium
View SolutionVedclass 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