Class 11 System of Particles and Rotational Motion worksheet

Sample questions

Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.

Section A · multiple choice

1. 1.

   Masses of 2 kg and 6 kg are 9 m apart. The centre of mass is at what distance from the 2 kg mass?

   1. 4.5 m
   2. 2.25 m
   3. 7.75 m
   4. 6.75 m

   Answer

   (d) 6.75 m

   x = m₂d/(m₁ + m₂)

2. 2.

   A force of 37 N acts at 1.9 m from the axis, at 0° to the line joining the axis to the point. The torque is:

   1. 70.3 N m
   2. 140.6 N m
   3. 0 N m
   4. 19.47 N m

   Answer

   (c) 0 N m

   τ = rF sin θ

3. 3.

   The moment of inertia of a uniform disc about its axis, of mass 4 kg and radius 1 m, is:

   1. 3 kg m²
   2. 1 kg m²
   3. 4 kg m²
   4. 2 kg m²

   Answer

   (d) 2 kg m²

   I = ½MR²

Section B · short answer

1. 4.

   Masses of 1 kg at (1, 1), 4 kg at (2, −3), 4 kg at (5, 4) (in metres). Find the centre of mass.

   Answer

   (29/9, 5/9) m

   x = Σmx/Σm, y = Σmy/Σm, Σm = 9

2. 5.

   A wheel starts at 15 rad/s and has a constant angular acceleration of 2 rad/s². Find its angular velocity after 8 s and the angle turned through.

   Answer

   31 rad/s; 184 rad

   ω = ω₀ + αt; θ = ω₀t + ½αt²

Section C · long answer

1. 6.

   A flywheel of moment of inertia 3.4 kg m², starting from rest, is acted on by a constant torque of 8 N m for 8 s. Find (a) the angular acceleration, (b) the final angular speed, (c) the angle turned through, (d) the work done by the torque, (e) the final kinetic energy.

   Answer

   (a) 2.35 rad/s²; (b) 18.82 rad/s; (c) 75.29 rad; (d) 602.35 J; (e) 602.35 J (equal to the work done)

   W = τθ = ½Iω²

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In the app, every System of Particles and Rotational Motion sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.

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