GUJCET Rotational Motion — practice questions
64 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice GUJCET Rotational Motion in the app →The moment of inertia of a solid sphere of mass $M$ and radius $R$ about a diameter is:A particle of mass $m$ moves in a circle of radius $R$ with constant speed $v$. Its angular momentum about theA solid sphere of mass $M$ and radius $R$ rolls without slipping on a horizontal surface with translational spA thin uniform rod of mass $M$ and length $L$ rotates about an axis perpendicular to the rod and passing throuA solid sphere is released from rest at the top of an incline of angle $\theta$. If it rolls without slipping A solid disc and a thin ring, having the same mass and same radius, are released from rest at the top of the sThe **moment of inertia** of a thin uniform rod of mass $M$ and length $L$ about a perpendicular axis through The **angular momentum** of a particle of momentum $\vec p$ at position $\vec r$ (from origin) is:For a body **rolling without slipping** on a flat surface with centre-of-mass velocity $v$, the **velocity of A solid sphere ($I = \tfrac{2}{5}MR^2$) rolls without slipping down a plane inclined at $\theta$. Its **linearBy **parallel-axis theorem**, the moment of inertia of a thin ring of mass $M$, radius $R$, about a tangent inAn ice-skater spinning with arms extended ($I_1 = 4$ kg·m², $\omega_1 = 3$ rad/s) pulls her arms in to $I_2 = A uniform rod of length $L$ is suspended from one end. Its **time period** for small oscillations is:A coin sits at distance $r$ from the centre of a turntable rotating with angular speed $\omega$. The **maximumAn Atwood machine: masses $m_1 > m_2$ over a **massive** pulley (uniform disc, mass $M$, radius $R$, $I = MR^2Four objects roll without slipping down an identical incline from the same height: **solid sphere, solid cylinA **solid sphere** rolling without slipping enters a vertical loop of radius $R$. The **minimum height** $h$ fTwo coaxial discs ($I_1, I_2$ with angular velocities $\omega_1, \omega_2$) are suddenly coupled. **Energy disA **yo-yo** (solid uniform cylinder) of mass $M$, radius $R$ unwinds under gravity. Its downward acceleration A billiard ball of radius $R$, mass $m$ at rest is struck horizontally by an impulse $J$ at height $h$ above iA **uniform cube** of side $a$ sits on a rough incline. As $\theta$ is increased, the cube **topples** before A solid sphere rolls at speed $v$ on a horizontal surface and elastically collides with an identical stationarA **disc** of mass $M$, radius $R$ rolls without slipping. A particle of mass $m$ rests on its **top** (sticksA thin **rod of length $L$, mass $M$** is hinged at one end and held horizontally; released from rest. The **aA **uniform sphere** of radius $R$ and mass $M$ is placed inside a fixed hemispherical bowl of radius $5R$. FoA man of mass $m$ stands at the edge of a horizontal platform (mass $M$, radius $R$, moment $I = \tfrac{1}{2}MA **bullet** of mass $m$, velocity $v$ strikes the lower end of a uniform rod (mass $M$, length $L$, hinged atA **hollow sphere** ($I = \tfrac{2}{3}MR^2$) and a **solid sphere** of equal mass and radius roll without slipA wheel of radius $R$ rolls without slipping at speed $v$. The **velocity** of a point on the rim at angle $\pA horizontal disc of mass $M$, radius $R$ spins freely at $\omega$. A second identical disc is dropped verticaA solid sphere is placed on a horizontal surface with **initial linear velocity $v_0$ (forward) and zero angulA spool of inner radius $r$ and outer radius $R$ ($r < R$) rests on a rough horizontal floor. A thread is pullA child of mass $m$ runs tangentially at speed $v$ and jumps on the rim of a stationary playground merry-go-roA uniform circular disc of radius $R$ and mass $M$ has a circular hole of radius $R/2$ cut out, **centred** atAngular displacement theta in a circular motion is related to arc length s and radius r as:Angular velocity omega in terms of time period T:Linear speed v and angular speed omega relation for circular motion:Torque tau acting on a body produces:Angular momentum L of a body rotating with angular velocity omega:A wheel starting from rest reaches 20 rad/s in 4 s. Angular acceleration alpha:Moment of inertia of a uniform solid sphere of mass M and radius R about an axis through center:Moment of inertia of a thin uniform disc (mass M, radius R) about axis perpendicular to disc through center:Parallel axis theorem states I_parallel = I_cm + Md². Here d is:For a thin rod of mass M and length L, I about axis through center perpendicular to rod:Kinetic energy of a rotating body with moment of inertia I and angular velocity omega:For a body rolling without slipping with velocity v of center of mass:A solid cylinder and a hollow cylinder of same mass and radius roll down an incline. Which reaches bottom firsTwo point masses 3 kg each at the ends of a massless rod of length 4 m. I about axis through center perpendicuA figure skater pulls in her arms during a spin. Her moment of inertia decreases. By conservation of L (I × omFor a hoop, disc, and solid sphere of same mass and radius rolling down an incline. Order of acceleration (fasA solid sphere of mass M, radius R rolls without slipping down an incline of angle theta. Acceleration:Two point masses 3 kg each at the ends of a massless rod of length 4 m. I about axis through center perpendicuFor a thin rod (mass M, length L) about axis through ONE END perpendicular to rod, I equals:Torque on a body produces angular acceleration. For tau = 20 N m and I = 5 kg m², alpha equals:A 50 kg flywheel of radius 0.5 m rotates at 60 rev/min. Angular momentum (I = MR²/2):A solid sphere rolls down without slipping. Fraction of KE that is rotational:A man stands at center of a rotating platform with hands extended (I_initial). He brings hands closer to body A wheel rotating at 50 rad/s decelerates uniformly to rest in 10 s. Total angular displacement:Angular acceleration alpha = 4 rad/s² acts for 5 s on a wheel starting from rest. Number of revolutions:For a body rotating at constant angular velocity omega, the linear speed at distance r from the axis is v = omA solid cylinder (I = MR²/2) of mass 2 kg, radius 0.1 m, rolls without slipping at 6 m/s. Total kinetic energyA merry-go-round (I = 1000 kg m²) rotates at 0.5 rad/s. A 50 kg child runs and jumps onto it at radius 2 m. NeFor a solid cylinder rolling without slipping, the friction force at the contact point:Moment of inertia of an annular disc (inner radius r1, outer r2) about perpendicular axis through center: