Ch 06 - System Of Particles And Rotational Motion11th Physics
Pure Translation vs. Pure Rotation
How do you precisely distinguish between pure translational motion and pure rotational motion of a rigid body in terms of particle velocities?
How do you precisely distinguish between pure translational motion and pure rotational motion of a rigid body in terms of particle velocities?
Pure Translation:
- Every single particle of the rigid body moves with the exact same linear velocity () at any given instant of time.
Pure Rotation:
- Every particle moves in a circle, which lies in a plane perpendicular to the axis of rotation.
- All particles share the same angular velocity (), but their linear velocities differ based on their perpendicular distance from the fixed axis.
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Centre of Gravity vs. Centre of Mass
How does the Centre of Gravity (CG) fundamentally differ conceptually from the Centre of Mass (CM) of a body?
How does the Centre of Gravity (CG) fundamentally differ conceptually from the Centre of Mass (CM) of a body?
Centre of Mass (CM):
- Represents the point where the entire mass of the body seems concentrated. It depends solely and entirely on the mass distribution of the body. It has nothing to do with gravity.
Centre of Gravity (CG):
- Represents the point where the total gravitational torque on the body evaluates to zero.
- Boundary Exception: The CG precisely coincides with the CM only if the gravitational field () is uniform across the entire body. For extremely massive extended bodies (like a mountain), varies, causing the CG to shift slightly away from the CM.
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Centre of Mass (Two-Particle System)
Centre of Mass (Two-Particle System)
State the formula for the position of the Centre of Mass (X) for a two-particle system aligned on the x-axis.
Variables & Units:
- X = Position of the centre of mass (m)
- = Masses of the individual particles (kg)
- = Positions of the particles from the origin (m)
Conditions/Notes:
- The centre of mass acts as a mass-weighted mean of positions.
- If the masses are exactly equal (), the centre of mass lies exactly midway between them: .
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Also in this chapter
46 more cards to study in Prism
- 4Precession in Rotational Motion
- 5Centre of Mass (Vector Form for n-Particles)
- 6Centre of Mass (Continuous Distribution)
- 7Velocity of Centre of Mass
- 8Centre of Mass of Symmetric Bodies
- 9Newton's 2nd Law for a System of Particles
- 10Conservation of Linear Momentum (System of Particles)
- 11Vector (Cross) Product
- 12Exploding Projectile Trajectory
- 13Cross Product & Area of a Triangle
- 14Right-Hand Screw Rule
- 15Linear and Angular Velocity Relation
- 16Angular Acceleration
- 17Torque (Moment of Force)
- 18Angular Momentum of a Particle
- 19Relation Between Torque & Angular Momentum
- 20Force Couple
- 21Mechanical Equilibrium of a Rigid Body
- 22Moment of Inertia
- 23Kinetic Energy of Rotation
- 24Radius of Gyration
- 25Theorem of Perpendicular Axes
- 26Theorem of Parallel Axes
- 27Moment of Inertia: Thin Ring
- 28Moment of Inertia: Uniform Disc / Solid Cylinder
- 29Moment of Inertia: Thin Rod
- 30Moment of Inertia: Solid Sphere
- 311st Equation of Rotational Kinematics
- 322nd Equation of Rotational Kinematics
- 333rd Equation of Rotational Kinematics
- 34Work Done by a Torque
- 35Instantaneous Rotational Power
- 36Newton's 2nd Law for Rotational Motion
- 37Kinetic Energy of a Rolling Body
- 38Rolling down an Inclined Plane (Velocity)
- 39Conservation of Angular Momentum
- 40Moment of Inertia: Thin Spherical Shell
- 41Angular Momentum Components (Fixed Axis)
- 42Moment of Inertia: Rectangular Plate
- 43Kinematics of Pure Rolling
- 44Separation of Kinetic Energy
- 45Instantaneous Axis of Rotation
- 46Separation of Angular Momentum
- 47Angular Impulse
- 48Work Done by Friction in Pure Rolling
- 49Acceleration in Rolling Down an Incline
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