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 $\mu_s \geq \left( \frac{\tan \theta}{1 + \frac{R^2}{K^2}} \right)$.
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