Mechanics Of Rotational Motion.

Question 1

What is the moment of inertia of a thin rod about an axis through its centre ?

Answer 1

i= ml^/12

Question 2

What is the moment of inertia of a thin rod about an axis passing through its corner ?

Answer 2

I= ml^/3

Question 3

What is the moment of inertia of a very thin circular loop ?

Answer 3

I= MR^

Question 4

What is the moment of inertia of a very thin spherical shell?

Answer 4

I=2/3 MR^

Question 5

What is the moment of inertia of a thin rectangular sheet ?

Answer 5

I= M a^+b^/12

Question 6

What is the moment of inertia of a uniform thin cone?

Answer 6

I= 3/10 MR^

Question 7

What is the moment of inertia of a thin circular sheet ?

Answer 7

I= 1/4 MR^

Question 8

What is the moment of inertia of a uniform thin rod ?

Answer 8

I= 1/3 MR^

Question 9

What are the two theorems of rotational motion ?

Answer 9

Theorem of Parallel axis and theorem of perpendicular axis

Question 10

What is the theorem of parallel axis ?

Answer 10

I= I(cm) + mr^

Question 11

What is theorem of perpendicular axis ?

Answer 11

This theorem is applicable for only a two dimensional body of negligible thickness. I(z)=I(x)+I(y)

Question 12

What is radius of gyration ?

Answer 12

It’s an imaginary distance form the axis at which whole mass of a Rigid body if kept at a point mass , moment of inertia remains unchanged b

Question 13

What is the formula for radius of gyration ?

Answer 13

I=mK^

Question 14

When is a body said to be a rigid body ?

Answer 14

If the distance between any two particles remains constant , body is said to be made up of a rigid body.

Question 15

What are the three types of motion of a rigid body ?

Answer 15

Only translational motion and only rotational motion and lastly both translational and rotational motion.

Question 16

Why is the formula of angular velocity?

Answer 16

v= r ω

Where v= linear speed of particle.

Question 17

What is centripetal acceleration ?

Answer 17

a(r)= ω²r= v²/r.
Centripetal is acceleration directed towards the centre. Note that speed remains constant , but direction changes continuously hence there is acceleration.

Question 18

Why is centripetal force ?

Answer 18

F= mv^/r. Since this resultant force is directed towards the centre, it’s called centripetal force. It’s required to keep the particle in uniform circular motion.

Question 19

What is centrifugal force ?

Answer 19

Centrifugal force is a pseudo force which acts on a particle away the centre (radially outward ) and has a magnitude mω²r.

Question 20

What is the formula for radial acceleration and tangential acceleration ?

Answer 20

a(r)= ω²r= v²/r.

a(t)=rα

Question 21

What is the minimum value of coefficient of friction required for pure rolling ?

Answer 21

μ(min)=(tan #)/(1+mR²/l)

Question 22

In motion of a spherical body on a rough inclined surface , if μ>μ(min), body with roll down without slipping without slipping with what acceleration ?

Answer 22

a₂=g sin #÷1+mR²/l

Force = ma₂

Question 23

If μ=0, body will slip downwards with what acceleration ?

Answer 23

a(1) = g sin #

Question 24

If μ

Answer 24

a₃=g sin # - μg cos #

Question 25

What is angular impulse ?

Answer 25

Linear impulse when multiplied by perpendicular distance gives angular impulse. Angular impulse = Change in angular momentum = Iω