Mechanics Of Rotational Motion. Flashcards Preview

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Flashcards in Mechanics Of Rotational Motion. Deck (25):
1

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

i= ml^/12

2

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

I= ml^/3

3

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

I= MR^

4

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

I=2/3 MR^

5

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

I= M a^+b^/12

6

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

I= 3/10 MR^

7

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

I= 1/4 MR^

8

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

I= 1/3 MR^

9

What are the two theorems of rotational motion ?

Theorem of Parallel axis and theorem of perpendicular axis

10

What is the theorem of parallel axis ?

I= I(cm) + mr^

11

What is theorem of perpendicular axis ?

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

12

What is radius of gyration ?

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

13

What is the formula for radius of gyration ?

I=mK^

14

When is a body said to be a rigid body ?

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

15

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

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

16

Why is the formula of angular velocity?

v= r ω
Where v= linear speed of particle.

17

What is centripetal acceleration ?

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.

18

Why is centripetal force ?

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.

19

What is centrifugal force ?

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

20

What is the formula for radial acceleration and tangential acceleration ?

a(r)= ω²r= v²/r.
a(t)=rα

21

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

μ(min)=(tan #)/(1+mR²/l)

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 ?

a₂=g sin #÷1+mR²/l
Force = ma₂

23

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

a(1) = g sin #

24

If μ

a₃=g sin # - μg cos #

25

What is angular impulse ?

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