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