ROTATION OF A RIGID BODY

1. 3.Rotational dynamics

1.1. Moment of inertia,I = ∑_(i=1)^n▒m_(i r^2 )

1.1.1. The sum of the products of the mass of each particle and the square and its respective distance from the rotation axis.m

1.1.2. scalar quantity

1.1.3. unit- kilogram metre square

1.1.4. Factors that affect I

1.1.4.1. mass of the body

1.1.4.2. shape of the body

1.1.4.3. position of the rotation axis

1.2. Στ=Iα

2. 2.Equilibrium of a uniform rigid body

2.1. Torque,τ ⃗ = r ⃗ × F ⃗

2.1.1. The product of a force and its perpendicular distance from the line of action of the force to the point (rotation axis)m

2.1.2. Rigid body,ΣF ⃗ =F_(nett )= 0

2.1.2.1. A body with definite shape that doesn’t change so that the particles that compose it stay in fixed position relative to one another even though a force is exert on it.

2.1.3. Centre of gravity, CG = the point at which the whole weight of the body may be considered to act

3. 1.Rotational kinematics

3.1. Average angular velocity,ωav= ∆θ/∆t,

3.1.1. The rate of change of angular displacement

3.1.2. Angular displacement,θ= s/r

3.1.2.1. An angle through which a point or line has been rotated in a specified direction in a specified axis.

3.1.2.2. unit in radian (rad)

3.1.3. Relationship between linear velocity, v and angular velocity,ω is v=rω

3.2. Instantaneous angular velocity ω= dθ/dt,

3.2.1. Instantaneous rate of change of angular displacement

3.2.2. vector quantity

3.2.3. radian per second

3.3. Instantaneous angular acceleration α= dω/dt,

3.3.1. The instantaneous rate of change of angular acceleration

3.3.2. vector quantity

3.3.3. radian per second per second

3.4. Average angular acceleration, αav = ∆ω/∆t

3.4.1. The rate of change of the angular velocity

3.4.2. radian per second per second

4. 4.Conservation of angular momentum

4.1. Angular momentum, L=Iω

4.1.1. The product of angular velocity of the body and its moment of inertia about the rotation axis.

4.1.2. vector quantity

4.1.3. unit- kilogram metre square per second

4.2. Relationship between angular momentum, L and linear momentum, p

4.2.1. A vector sums of all the torque acting on a rigid body ism proportional to the rate of change of the angular momentum

4.3. Relationship between angular momentum, L and linear momentum, p

4.3.1. Iω=constant if Στ ⃗ = 0