#### IIT (NTSE/Olympiad)

# Circular Motion & Rotational Dynamics

__Formulae For The Moment of Inertia of Regular Bodies__

__Formulae For The Moment of Inertia of Regular Bodies__

Shape of body | Axis of Rotation | Figure | Moment of Inertia (I) | Radius of Gyration (K) | |
---|---|---|---|---|---|

(1) Circular Ring, M :- Mass, R :- Radius | 1)Passes through the centre and perpendicular to the plane | MR^{2} | R | ||

2) About its Diameter in its own plane | R / √2 | ||||

3) About a tangential axis perpendicular to its own plane. | 2MR^{2} | √2R | |||

4) About a tangential axis in its own plane | MR^{2} | .R | |||

(2) Circular disc, M:- Mass, R:- Radius | 1) Passing through the centre and perpendicular to the plane | ||||

2) About Diameter | MR^{2}/4 | MR^{2} | R | ||

4) About a tangential axis Perpendicular to its own plane | MR^{2} | R | |||

3) Hollow Cylinder, M = Mass, R = Radius, L = Length | a) About its geometrical axis | MR^{2} | R | ||

b) About an axis passing through its CM and perpendicular to its length | |||||

c) About an axis perpendicular to its length and passing through one end of the cylinder | |||||

(4) Solid Cylinder, M:- Mass, R:- Radius, L:- Length | A) About its geometrical Axis | ||||

B) About an axis passing through its C.G. and Perpendicular to its axis | |||||

C) About the diameter of one of the faces of the cylinder and perpendicular to the length | |||||

(5) Solid Sphere, M:- Mass, R:- Radius | A) About its axis OR diameter, which is passing through centre. | ||||

B) About Tangential axis | |||||

(6) Thin Spherical Shell (Hollow Sphere), M: Mass, R: Radius, Thickness negligible | 1) Passing through axis or diameter | ||||

2) About Tangential Axis | |||||

(7) Solid sphere with cavity, Internal radius = r, Outer Radius = R, Mass :- M | About passing through centre OR about diameter | ||||

(8) Thin rod [thickness is negligible w.r.t. length] | 1) Passing through centre of mass and perpendicular to length | ||||

2) Passing through its one end and perpendicular to axis. | |||||

(9) Rectangular plate, a = Length, b = width, M = Mass | (a) About an axis passing through CM and perpendicular to side a in its plane. | ||||

b) about an axis passing through CM and perpendicular to side b in its plane. | |||||

c) About an axis passing through CM and |

#### IIT (Class X)

- Unit, Dimension & Error

- Vectors

- Motion in One Dimension

- PROJECTILE MOTION

- NEWTON'S LAWS OF MOTION & FRICTION

- WORK, POWER, ENERGY & CONSERVATION LAWS

- CIRCULAR MOTION & ROTATIONAL DYNAMICS
- 1. Angular Displacement
- 2. Angular Velocity
- 3. Relation Between Linear Velocity And Angular Velocity
- 4. Angular Acceleration
- 5. Relation Between Angular acceleration and Linear Acceleration
- 6. Equation of linear motion and rotational motion
- 7. Centripetal Acceleration and centripetal Force
- 8. Type of Circular Motion
- 9. Banking of Tracks
- 10. Moment of Inertia (Rotational inertia)
- 11. Torque
- 12. Forces Couple
- 13. Angular Momentum
- 14. Kinetic Energy of Rotation
- 15. linear and rolling motion of a body on inclined plane
- 16. Points to Remember - Circular Motion & Rotational Dynamics

- GRAVITATION