Class 12 Mathematics Complex Number+ Cube Root of Unity Complete Note NEB | Simple to Advance Problem Solved

 Class 12 Mathematics Complex Number Complete Note | Simple to Advance  Problem Solved

From this post ,you will learn about all basics to advance concept of Complex Number required for Class 12 Mathematics.

Pointwise:

• You will learn Complex Number in these 19 images below.
• You will learn also Cube Root of Unity in last 6 images.

Image Solutions :

Complex  Number:

Cube Root Of Unity:

highlighted portion should be (w²+w)

Lets summarize the whole lesson of Rotational Dynamics Class 12 through the question below.

1.) Compare the equation of angular motion with the equation of linear motion.

2.) Define angular momentum.A planet revolves around a massive star in a highly elliptical orbit.Is its angular momentum constant over the entire orbit?

3.) A disc of moment of inertia 5 x 10^-4 kg m^2 is rotating freely about axis O through its centre at 40 rpm as shown in figure.Calculate the new revolution per minute(r.p.m) if some wax of mass 0.02kg is dropped gently on to the disc 0.08m from its axis.

4.) Write a relation between  moment of inertia and torque.

5.) Describe the work and power in rotational motion with their expression.

6.) A mass of 2kg is rotating on a circular path of radius 0.8m with angular velocity of 14 rad s-1.If the radius of the path become 1m,what will be the value of angular velocity.

7.) A string of wrapped around the rim is wheel of moment of inertia 0.20 kg m^2 and radius 20cm.The wheel is free to rotate about its axis as in figure.Initially the wheel is at rest.The string is now pulled by a force of 20N.Find the angular velocity of the wheel after 5 seconds.

8.) Define the term moment of inertia and radius of gyration.

 9.) A ballet dancer spins about a vertical axis at 1rps with her arms outstretched with her arm folded her moment of inertia about the vertical axis decreases by 60%.Calculate the new rate of revolution.

10.) Define moment of Inertia of a  rigid body.Give its unit and the dimensional formula.

11.) Explain the term torque and angular momentum and obtain the relation between them.

12.) What is the kinetic energy of a rotating body.Derive an expression for it

13.)Show that in rotational motion,power is the product of torque and angular velocity

14.) The angular velocity of a wheel increases from 1200 to 4500 rev/min in 10 sec.Compute its angular acceleration and number of revolution during this time.

15.) Define torque.A wrench of longer arm is preffered than a wrench of shorter arm,why?explain.

 16.) A flywheel of a gasoline engine is required to give up 500J of kinetic energy while its angular velocity decreases from 650 rev/min to 520 rev/min.What moment of inertia is required? 

17.) Establish the relation between torque and angular acceleration of rigid body

18.) State and prove the principle of conservation of angular momentum

19.) Forces F1=7.5N and F2=5.3N are applied tangentially to a wheel with radius 0.33m as shown in figure.What is the net torque on the wheel due to these two forces for an axis perpendicular to the wheel and passing through its center?

20.) A disc of mass 2kg and radius 20cm is free to rotate about an axis through it centre and perpendicular to the disc.If a force of 50N is applied tangentially.Calculate the angular acceleration

 21.) A wheel starting from rest is rotating with a constant angular acceleration of 3.0 rad s^-2.An observer notes that it traces an angle of 120 radiation in 40 second interval.For how long the wheel had been rotated when the observer started his observation?

22.) A flywheel has moment of intertia of 4kg m^-2 about an axis through its centre and is rotating 120 revolution per minute.What constant opposing torque is required to bring it at rest in 5 second?

 23.) A constant torque of 20Nm is exerted on a pivoted wheel for 10 second during which time the angular velocity of the wheel changes from zero to 100rpm.When the external torque is removed,it is stopped by friction in 100sec.Find

24.) Define the term couple and moment of couple.Derive the expression for the work done by a couple