Get 65% Discount on Preventive Health Checkup
Career in India        

MHT-CET : Physics Entrance Exam

MHT - CET : Physics - Rotational Motion Formulae Page 1

‹‹ Previous  |  Formulae Page 1  |  Next ››



1. Coordinates of the centre of mass

 

 

 

x =

n

mixi

i = 1

n

mi

i = 1

where xi  yi and zi are the x  y and z co-ordinates
respectively, of the ith particle and m
i is its mass.

y =

n

miyi

i = 1

n

mi

i = 1

O

z =

n

mizi

i = 1

n

mi

i = 1

 

 

2. Position Vector of the Centre of Mass

 





=

n

mii

i = 1

M

where is the position vector of the ith particle
and M is the mass of the body.

 

 

3. Position Vector for a Rigid Body

 

=

1

M

  dm

where is the position vector of an element of mass dm.

 

 

4.

 

Moment of inertia, I =

n

mir2i

i = 1

.

 

5.

 

Radius of gyration (K) is given by the relation I = MK2

 

\ K =

 where I is the moment of inertia and M is the mass of the body.

 

6.

 

Kinetic energy of a rotating body, E =

1

2

Iw2


where I is the moment of inertia and w is the angular velocity of the rotating body.

 

7.

 

Torque acting on a rotating body, T = Ia where a is the angular acceleration of the body.

 

8.

 

Principle of parallel axes states that, I0 = Ic + Mh2 where I0 is the M.I. about an axis through 0, Ic is the M.I. about an axis through the centre of mass, M is the mass of the body and h is the distance between the two parallel axes.

 

9.

 

Principle of perpendicular axes states that Iz = Ix + Iy where Ix, Iy and Iz are the moments of inertia about the X, Y and Z axes of a plane lamina such that X and Y axes lie in the plane of the lamina, and Z axis is perpendicular to the plane.

 

10.

 

M.I. of a thin uniform rod rotating about a perpendicular axis through its middle

I =

Ml 2

12

,

K =

l

 

 

11.

 

M.I. of a thin uniform rod rotating about a perpendicular axis through one end

I =

Ml 2

3

,

K =

l

 

 

12.

 

M.I. of a thin uniform disc rotating about an axis passing through its centre and perpendicular to its plane,

I =

MR2

2

,


K =

R

 

(Note: This formula can also be applied to a cylinder or coin)

 

13.

 

M.I. of a thin uniform disc rotating about a diameter,

I =

MR2

4

,

K =

R

2

 

 

14

 

  Angular momentum L = Iw where I is the moment of inertia and w is the angular velocity.

 

15

Equations of rotational motion of a body are

where q is the angular displacement,
w0 and wt are the angular velocities at t= 0 and t =t, respectively, and a is the angular acceleration

a) wt =w0 + at

 

b) q = w0t +

1

2

at2

c) wt2 = w20 + 2 aq

 

16

 

Moment of inertia of a ring = MR2              R radius of ring

 

17

 

M.I. of a hollow sphere =

2

3

MR2

 

18

 

M.I. of a solid sphere =

2

5

MR2

 

19

 

Total K.E. of a rolling body =

1

2

mv 2 +

1

2

Iw2

 

 

For a disc: total K.E. =

1

2

mv 2+

1

4

mv 2=

3

4

 mv 2

 

 

 

For a ring: total K.E. =

1

2

mv 2+

1

2

mv 2=

 mv 2

 

 

 

For a sphere: total K.E.=

1

2

mv 2+

2

10

mv 2=

7

10

 mv 2

 

 

‹‹ Previous  |  Formulae Page 1  |  Next ››


Career in India | Jobs in India
© All Rights Reserved, indicareer.com | partners | Sitemap