This article contains Rotational motion practice problems for class 11. In this article I have given definition and derivation based problems, very short answer type questions , short answer type questions.
You can print this article and practice these problems.
You read notes on this chapter before practicing these questions. For them please visit this link
Center of Mass
Rotational Motion
Other assignments(Included with Linear momentum) for this chapter which you can have a look are
Rotational Motion Multiple Choice Questions
Rotational Motion Problems
Center of Mass Problems with Solutions
The Class 11 questions usually cover areas like:
- Moment of Inertia: Calculating the moment of inertia for various objects like rods, discs, and spheres, often involving integration for continuous bodies.
- Angular Momentum: Understanding the conservation of angular momentum, its calculation for different rotating bodies, and solving problems involving collisions or other interactions.
- Torque and Angular Acceleration: Questions might involve calculating the torque exerted by forces and relating it to angular acceleration using Newton’s second law for rotation.
- Rotational Kinematics: Problems involving angular velocity and angular acceleration, similar to linear kinematics but in the rotational context.
- Rotational Energy: Calculating rotational kinetic energy and solving problems involving energy conservation with both rotational and translational motion.
- Combined Translation and Rotation: Problems where objects are rolling, such as cylinders or spheres rolling down inclined planes, requiring understanding of both translational and rotational motion.
Rotational motion practice problems
Q 1. Define center of mass and center of gravity.
Q 2. Make a table showing COM of following regular symmetrical bodies.
- Thin rod
- Ring
- Disc
- Rectangular lamina
- Cubical block
- Cylinder
- Sphere
- Triangular lamina
- Right circular cone
Also draw their respective diagrams pointing out position of COM in respective bodies.
Q 3. Derive three equation of rotational motion under constant angular acceleration from first principle.
Q 4. On what factor does the turning effect of a force depend ? What is the turning effect of a force called?
Q 5. Define term torque or moment of force . Give its units and dimensions.
Q 6. State and explain the principle of moments of rotational equilibrium.
Q 7. What is a couple? What effect does it have on a body ? Show that the moment of couple is same irrespective of the point of rotation of a body.
Q 8. In the HCL molecule, the separation between the nuclei of the two atoms is 1.27 A. Calculate the approximate location of the center of mass of the molecule. Given: Chlorine atom is heavier and 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus. (Ans:- 1.235$\AA$)
Q 9. What will be the nature of motion of center of mass of an isolated system .
Q 10. The motor of an engine is rotating about its axes with an angular velocity of 120 r.p.m. It comes to rest in IOS, after being switched off. Assuming constant deceleration, calculate the number of revolutions made by it before coming to rest. (Ans:- 10)
MCQ Questions
Q 11 A solid sphere, a hollow sphere, and a ring are all of the same mass and radius. Which one has the highest moment of inertia about an axis passing through its center and perpendicular to its plane?
a) Solid Sphere
b) Hollow Sphere
c) Ring
d) All have the same moment of inertia
Answer
(c) Ring
The moment of inertia depends on both the mass distribution and the axis of rotation. For objects with the same mass and radius, the moment of inertia is greatest for the object with the mass furthest from the axis. In this case, the ring has all its mass at the maximum distance from the center, hence the highest moment of inertia.
Q 12 If the torque acting on a body is doubled, and its moment of inertia is halved, the angular acceleration will:
a) Remain the same
b) Double
c) Quadruple
d) Become half
Answer
(c) Quadruple
Angular acceleration ($ \alpha $) is given by $ \alpha = \tau / I $, where $ \tau $ is the torque and $ I $ is the moment of inertia.
If torque is doubled and moment of inertia is halved, $ \alpha $ becomes $ 2\tau / (I/2) = 4\tau / I $, which is four times the original angular acceleration.
Q 13 A wheel makes 360 revolutions in one minute. What is its angular velocity in radians per second?
a) $ 2\pi $ rad/s
b) $ 12\pi $ rad/s
c) $ 6\pi $ rad/s
d) $ 24\pi $ rad/s
Answer
(b) $ 12\pi $ rad/s
360 revolutions per minute mean 6 revolutions per second (since there are 60 seconds in a minute). Each revolution is $ 2\pi $ radians, so the angular velocity is $ 6 \times 2\pi = 12\pi $ radians per second.
Q 14 A figure skater spins at a certain angular velocity with her arms extended. When she pulls her arms in, her moment of inertia decreases, and her angular velocity:
a) Decreases
b) Increases
c) Remains constant
d) Becomes zero
Answer
(b) Increases
According to the conservation of angular momentum, if no external torque acts on a system, the angular momentum remains constant. Angular momentum $ L $ is the product of moment of inertia $ I $ and angular velocity $ \omega $ ($ L = I\omega $). If the skater pulls her arms in, her moment of inertia decreases, so her angular velocity must increase to keep $ L $ constant.
Q 15 Which of the following statements is true about the rotational kinetic energy of a rotating object?
a) It is directly proportional to the square of its angular velocity.
b) It is directly proportional to the square of its radius.
c) It is inversely proportional to its moment of inertia.
d) It does not depend on the shape of the object.
Answer
(a) It is directly proportional to the square of its angular velocity.
Rotational kinetic energy is given by $ \frac{1}{2} I \omega^2 $, where $ I $ is the moment of inertia and $ \omega $ is the angular velocity.
This formula shows that the rotational kinetic energy is directly proportional to the square of the angular velocity.
Q 16.A cylinder is rolling without slipping on a horizontal surface. The ratio of its translational kinetic energy to its rotational kinetic energy is:
a) 1:1
b) 1:2
c) 2:1
d) 1:4
Answer
(b) 1:2
For a cylinder rolling without slipping, the translational kinetic energy is $ \frac{1}{2} mv^2 $ and the rotational kinetic energy is $ \frac{1}{2} I \omega^2 $.
For a solid cylinder, $ I = \frac{1}{2} mr^2 $ and $ \omega = v/r $.
Substituting these in, the rotational kinetic energy becomes $ \frac{1}{4} mv^2 $.
Thus, the ratio of translational to rotational kinetic energy is
$ \frac{1}{2} mv^2 : \frac{1}{4} mv^2 = 1:2 $.
Q 17.For which of the following does the centre of mass lie outside the body ?
(a) A pencil
(b) A shotput
(c) A dice
(d) A bangle
Answer
(d)
Q 18. The net external torque on a system of particles about an axis is zero. Which of the following are compatible with it ?
(a) The forces may be acting radially from a point on the axis.
(b) The forces may be acting on the axis of rotation.
(c) The forces may be acting parallel to the axis of rotation.
(d) The torque caused by some forces may be equal and opposite to that caused by other forces.
Answer
All of the above are true
Some other resources you can look for reference are https://en.wikipedia.org/wiki/Center_of_mass https://www.khanacademy.org/science/physics/linear-momentum/center-of-mass/a/what-is-center-of-mass http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html Hope you like this Rotational motion practice problems and these help you in your exams. If you like this article please share it among your friends.