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VITEEE Systems of Particles and Rotational Motion — practice questions

Explore 57 free Systems of Particles and Rotational Motion questions in VITEEE Physics. Open each question or exercise to read its content, reference answers and available explanation.

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Systems of Particles and Rotational Motion questions and exercises with answers

Showing questions 1–30 of 57.

The moment of inertia of a solid sphere of mass $M$ and radius $R$ about a diameter is:Read the answer and worked solution →Angular displacement theta in a circular motion is related to arc length s and radius r as:Read the answer and worked solution →Angular velocity omega in terms of time period T:Read the answer and worked solution →Linear speed v and angular speed omega relation for circular motion:Read the answer and worked solution →Torque tau acting on a body produces:Read the answer and worked solution →Angular momentum L of a body rotating with angular velocity omega:Read the answer and worked solution →A wheel starting from rest reaches 20 rad/s in 4 s. Angular acceleration alpha:Read the answer and worked solution →Moment of inertia of a uniform solid sphere of mass M and radius R about an axis through center:Read the answer and worked solution →Moment of inertia of a thin uniform disc (mass M, radius R) about axis perpendicular to disc through center:Read the answer and worked solution →Parallel axis theorem states I_parallel = I_cm + Md². Here d is:Read the answer and worked solution →For a thin rod of mass M and length L, I about axis through center perpendicular to rod:Read the answer and worked solution →Kinetic energy of a rotating body with moment of inertia I and angular velocity omega:Read the answer and worked solution →For a body rolling without slipping with velocity v of center of mass:Read the answer and worked solution →A solid cylinder and a hollow cylinder of same mass and radius roll down an incline. Which reaches bottom first?Read the answer and worked solution →Two point masses 3 kg each at the ends of a massless rod of length 4 m. I about axis through center perpendicular to rod:Read the answer and worked solution →A figure skater pulls in her arms during a spin. Her moment of inertia decreases. By conservation of L (I × omega), her angular velocity:Read the answer and worked solution →For a hoop, disc, and solid sphere of same mass and radius rolling down an incline. Order of acceleration (fastest first):Read the answer and worked solution →A solid sphere of mass M, radius R rolls without slipping down an incline of angle theta. Acceleration:Read the answer and worked solution →Two point masses 3 kg each at the ends of a massless rod of length 4 m. I about axis through center perpendicular to rod:Read the answer and worked solution →For a thin rod (mass M, length L) about axis through ONE END perpendicular to rod, I equals:Read the answer and worked solution →Torque on a body produces angular acceleration. For tau = 20 N m and I = 5 kg m², alpha equals:Read the answer and worked solution →A 50 kg flywheel of radius 0.5 m rotates at 60 rev/min. Angular momentum (I = MR²/2):Read the answer and worked solution →A solid sphere rolls down without slipping. Fraction of KE that is rotational:Read the answer and worked solution →A wheel rotating at 50 rad/s decelerates uniformly to rest in 10 s. Total angular displacement:Read the answer and worked solution →Angular acceleration alpha = 4 rad/s² acts for 5 s on a wheel starting from rest. Number of revolutions:Read the answer and worked solution →A solid cylinder (I = MR²/2) of mass 2 kg, radius 0.1 m, rolls without slipping at 6 m/s. Total kinetic energy:Read the answer and worked solution →For a solid cylinder rolling without slipping, the friction force at the contact point:Read the answer and worked solution →Moment of inertia of an annular disc (inner radius r1, outer r2) about perpendicular axis through center:Read the answer and worked solution →NEET · Physics · Moment of Inertia — Standard ShapesRead the answer and worked solution →NEET · Physics · Centre of MassRead the answer and worked solution →

Worked practice questions

The moment of inertia of a solid sphere of mass $M$ and radius $R$ about a diameter is:

  1. $\dfrac{1}{2}MR^2$
  2. $\dfrac{2}{3}MR^2$
  3. $\dfrac{2}{5}MR^2$
  4. $MR^2$
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Correct answer: C. $\dfrac{2}{5}MR^2$

Standard result for a solid sphere about a central axis: $I = \dfrac{2}{5}MR^2$. Compare with a hollow (thin-shell) sphere where $I = \dfrac{2}{3}MR^2$ — that's option D and a common trap.

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Angular displacement theta in a circular motion is related to arc length s and radius r as:

  1. theta = s + r
  2. theta = r / s
  3. theta = s × r
  4. theta = s / r
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Correct answer: D. theta = s / r

Angular displacement theta = s/r, measured in radians. For one full revolution, s = circumference = 2πr, giving theta = 2π.

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Angular velocity omega in terms of time period T:

  1. omega = 1/T
  2. omega = 2π/T
  3. omega = T
  4. omega = T/2π
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Correct answer: B. omega = 2π/T

omega = 2π/T = 2πf. SI unit: rad/s. T is time for one full rotation; one rotation is 2π rad.

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