# Rotational Dynamics Class 12 Physics Notes PDF

Rotational Dynamics Class 12 Physics Notes is very much helpful for grade 12 science students. Before we move towards the notes. Let's is know what rotational motion really means in short. Rotational motion is the study of rotational motion of a rigid body. A solid body in which the particles are compactly arranged and their positions are not disturbed by any external force applied on it is called rigid body.

However, no real body is truly rigid. For the study of rotational motion, all the solids are assumed as rigid body. Fluid (i.e. liquid and gas) are not rigid body as they do not have fixed shape. We must note that a rigid body may possess both translational and rotational motion.

In translational motion, a rigid body (C.M of the body) moves from one point to another point. Every particle in it has the same linear velocity and displacement. For example: a car moving in its path, th rigid body is said to be in rotational motion about its axis if all its particles rotate about an axis with the same angular velocity but different linear velocities. For example: the motion of a wheel of a train about its axle.

## Rotational Dynamics Class 12 Physics Notes

The PDFgiven below contains handwritten notes of class 12 rotational dynamics chapter. It includes equations of angular motion, Relation between linear and AngularKinetic Energy of Rotation of a body, kinematics, Moment of Inertia, Radius of Gyration and many more other subtopics related to class 12 rotational motion.

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Once you download the PDF of class 12 rotational dynamics, you can use it even if you are offline. It will provide you an opportunity to complete your notes without having to wait for internet connection.

## Rotational Dynamics Numericals Class 12

Once you complete your notes of rotational dynamics chapter. It is important to for you to solve plenty of numerical inorder to get perfect in rotational dynamics chapter. There are many formulas in rotational dynamics and you need to solve at least 2 numerical using each formula.

Now while solving numerical problem, you may stuck or may don't know how to start solving it. In that case, we have brought the solved numerical solutions. The PDF given below contains solved numerical problem which will help you to get the concept of solving numerical problems.

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If these numerical problems are not enough then you can try solving some other numericals from your set book or try solving numericals from the past year question paper. If you are still not perfect in solving the numericals then you can watch different videos available on YouTube.

## Rotational Dynamics Class 12 important short questions

Till now we have completed our notes and solved different numericals as well, but that's not enough. You need to study different short questions because they are very important for your exam. Short questions can be give reasons or writing the definitions of different terms.

We have collected some of the important short question answers and give reasons which were frequently asked in class 12 board exams.

**1. Why are spokes fitted in the wheel of bicycle?**

** Ans:** When spokes are fitted in the wheel of bicycle, it increases the moment of inertia of the wheel. As we know greater the moment of inertia, greater will be the opposition to any change in uniform rotational motion, which assures that the cycle moves smoother and steadier. That is why wheels are fitted with spokes.

**2. There are two spheres of same radius. One is solid and the other is hollow. Which one has greater moment of inertia?**

** Ans:** In case of hollow sphere most of the particles are in the longer distances from the axis of rotation as compared to the average distance of particles from axis in case of solid sphere. Therefore, hollow sphere has greater moment of inertia.

**3. Friction is necessary for the disc to roll on the surface in the straight line. Why? **

** Ans:** A disc will roll in a straight line only when a torque acts on it. Friction between the disc and the surface provides necessary tangential force. As a result of which torque acts on the disc. That is why friction is necessary to roll a disc on a surface in straight line.

**4. Why is a cat does not get injured while falling on ground?**

__ Ans:__ While falling from a height, cat stretches its body along with its tail, this increases moment of inertia. As there is no external torque acting, the angular momentum must remain constant (Iω = constant). Hence, when moment of inertia increases then to decreases. Therefore, cat can land gently on the ground.

**5. How can you distinguish a boiled egg and a raw egg? Explain**.

** Ans:** A raw egg and a boiled egg can be distinguished by spinning either of them on a smooth surface. Boiled egg has solid mass and hence has low moment of inertia, therefore will have greater angular velocity for a given torque. Whereas in the raw egg, the matter inside the egg is in liquid form so try to get away from axis thereby increasing moment of inertia of egg, which then decrease angular velocity. From these two observations we can distinguish raw and boiled egg.

**6. If radius of earth is halved keeping mass same, what would be the length of day?**

** Ans:** We have, moment of inertia of a sphere rotating about its axis as M.I. = 2/5MR². This equation shows that when radius of earth is halved, then M.I. of earth about its axis will become one fourth of its initial M.I. As we know the angular momentum of a body remains constant in absence of external torque, when M.I. increases to one fourth, to must increase four times. Hence earth can complete a rotation about its axis in 6 hours instead of 24 hours. Therefore, a day will be of 6 hours.

**7. A solid ball and a hollow ball with the same mass and radius roll down a slope. Which one reaches the ground first?**

** Ans:** As we know, the moment of inertia of hollow ball is greater than that of solid ball; the solid ball will have greater acceleration. Hence the solid ball will reach the ground first.

**8. A heavy wheel is attached to the shaft of engines. Why?**

** Ans:** When a heavy wheel is attached to the shaft of engines, its moment of inertia increases. Since, ω = L/I, any change in angular momentum imparted to the wheel results lesser change in angular velocity. And also increase in M.I. of it causes to store greater amount of kinetic energy.

**9. In a fly wheel, most of its mass is concentrated at its rim. Why?**

** Ans:** By concentrating most of the mass at the rim, a fly wheel acquires greater moment of inertia. For such a wheel which has greater moment of inertia, angular velocity changes very slowly and thus help to maintain uniform rotational motion.

**10. If the earth is struck by meteorites, the earth will slow down slightly. Why? **

** Ans:** When meteorites strike the earth, it will remain contained on earth and mass of earth increases. Hence moment of inertia of earth increases and due to which angular velocity decreases as the total angular momentum remains constant. Hence the earth slows down and so length of day increases.

**11. Why is it more difficult to revolve a stone by tying it to a loner string than by tying it to a shorter string? **

__ Ans:__ To produce an angular momentum acceleration a, the relation is given as torque = Iα, where I is the moment of inertia of the body given as I= MR². Hence, when the distance of stone increases, M.I. increases and so the torque required producing same angular acceleration increases. Therefore, it is difficult to revolve stone by tying it to a longer string than by tying it to a shorter stone.

**12. A helicopter is provided with two propellers. Give reason.**

__ Ans:__ If a helicopter contains only one propeller, then there will be chance that the helicopter turned in opposite direction because of conservation of angular momentum. Hence, a helicopter is provided with two propellers to balance it.

**13. Why the speed of a whirlwind in a tornado very high?**

__ Ans:__ In a whirlwind, the air from the surrounding gets more concentrated in a small region, due to which moment of inertia decreases. Since angular momentum is a conserved quantity, angular velocity must increase at the same time to a very high value.

**14. Ladder apt to slip more when you are high up on it than when you just begin to climb. Explain. **

__ Ans:__ When a man is high up on the ladder, the moment of force about the base increases due to increase in lever arm, which tends to rotate the ladder. But in case when a man just starts to climb, the ladder arm is small and the moment of force is also small. So do not tend to turn over the ladder.

**15. What is the counterpart of mass and force in rotational motion? **

** Ans:** Moment of inertia is counterpart of mass while torque is counterpart of force in rotational motion. This means moment of inertia player the same role in rotational motion as mass plays in linear motion while torque plays the same role in rotational motion as the force plays in linear motion.