Class 11PhysicsSystem of Particles and Rotational MotionMix Example - System of Particles and Rotational Motion
MediumState whether the following statements are true or false:
$(1)$ Torque produces angular velocity in an object.
$(2)$ For the rotational motion of a rigid body,the linear variables of all its particles are the same.
$(1)$ Torque produces angular velocity in an object.
$(2)$ For the rotational motion of a rigid body,the linear variables of all its particles are the same.
(N/A) $(1)$ False. Torque produces angular acceleration,not angular velocity.
$(2)$ False. In the rotational motion of a rigid body,all particles have the same angular variables (angular displacement,angular velocity,and angular acceleration),but their linear variables (linear displacement,linear velocity,and linear acceleration) differ depending on their distance from the axis of rotation.
$(2)$ False. In the rotational motion of a rigid body,all particles have the same angular variables (angular displacement,angular velocity,and angular acceleration),but their linear variables (linear displacement,linear velocity,and linear acceleration) differ depending on their distance from the axis of rotation.
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$A$ particle starts from the point $(0\,m, 8\,m)$ and moves with a uniform velocity of $3\, \hat{i} \,m/s$. After $5\,s$,the angular velocity of the particle about the origin will be:
Medium
View Solution$A$ solid sphere of radius $R$ has a moment of inertia $I$ about its geometric axis. It is melted and recast into a disc of radius $r$ and thickness $t$. If the moment of inertia of this disc about an axis tangent to its edge and perpendicular to its plane is also $I$,find the value of $r$.
Difficult
View SolutionState whether the following statements are True or False:
$(1)$ The angular acceleration of an object rotating with a constant angular velocity is always zero.
$(2)$ An object can have a moment of inertia without energy.
$(3)$ The radius of gyration of an object is a constant quantity.
$(4)$ $A$ figure skater spins faster when they pull their arms in because their moment of inertia decreases.
$(1)$ The angular acceleration of an object rotating with a constant angular velocity is always zero.
$(2)$ An object can have a moment of inertia without energy.
$(3)$ The radius of gyration of an object is a constant quantity.
$(4)$ $A$ figure skater spins faster when they pull their arms in because their moment of inertia decreases.
Medium
View Solution$A$ uniform sphere of mass $m$ and radius $R$ is placed on a rough horizontal surface. The sphere is struck horizontally at a height $h$ from the floor. Match the following:
$(a)$ $h = \frac{R}{2}$ $(i)$ Sphere rolls without slipping with a constant velocity and no loss of energy. $(b)$ $h = R$ $(ii)$ Sphere spins clockwise,loses energy by friction. $(c)$ $h = \frac{3R}{2}$ $(iii)$ Sphere spins anti-clockwise,loses energy by friction. $(d)$ $h = \frac{7R}{5}$ $(iv)$ Sphere has only a translational motion,loses energy by friction.
| $(a)$ $h = \frac{R}{2}$ | $(i)$ Sphere rolls without slipping with a constant velocity and no loss of energy. |
| $(b)$ $h = R$ | $(ii)$ Sphere spins clockwise,loses energy by friction. |
| $(c)$ $h = \frac{3R}{2}$ | $(iii)$ Sphere spins anti-clockwise,loses energy by friction. |
| $(d)$ $h = \frac{7R}{5}$ | $(iv)$ Sphere has only a translational motion,loses energy by friction. |
Medium
View SolutionAn object has a moment of inertia of $3 \ kg \cdot m^2$. It is rotating with an angular velocity of $2 \ rad/s$. If a mass of $12 \ kg$ is moving with a velocity of $v \ m/s$,at what value of $v$ will their kinetic energies be equal?
Medium
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