Mechanics of Rigid Bodies Flashcards
What is a rigid body?
A rigid body is a body with an axis of rotation and whose axis is stable.
What causes rotational motion?
Torque
What is the unit of Torque?
Nm
Name one special property of a rigid body.
It can perform both translational and rotational motion.
What causes rotational motion?
Torque
What is the moment of a vector?
The moment of a line vector r is the vector product of its magnitude and its perpendicular distance from its axis O the direction of r
What is torque?
It refers to the moment of a force.
What is angular momentum?
The moment about the origin of a linear momentum P which passes through a point with position vector r is given as L = r x P = mvr where L = angular momentum
What is a couple?
A couple refers to two equal and opposite forces whose lines of action do not coincide. These forces usually bring about a turning effect.
When is a rigid body said to be in equilibrium?
If the resultant force acting on it is zero. That means that it either remains at rest or in motion with constant velocity.
What is the condition for translational equilibrium?
When a body remains at rest or in motion with constant velocity
What is the centre of mass?
It is the unique point or location in space that represents the average position of its mass. It is the point at which an applied force produces acceleration but no rotation.
What is the COM of a 1-dimensional body?
It is the point at which it balances.
What is the COM of a 2-dimensional body?
It is the point at which it balances.
What is the COM of a 3-dimensional body?
It is the point at which for any axis passing through it, there is no tendency for gravity to rotate the body about that axis
What is the centre of gravity of a body?
It is the point where the resultant force of attraction is concentrated, i.e. where the weight is concentrated.
State the parallel axis theorem
According to parallel axis theorem, moment of inertia is the sum of moment of inertia through mass center and product of mass and square of perpendicular distance between mass center and rotation axis.
What is the radius of gyration?
It is the mass moment of inertia of a body about a specific axis.
Torque
Fr or Frsin@
Angular momentum
rP or rmv or mvr
COM
m1x1 + m2x2 + m3x3 / m1 + m2 + m3
COM for thin straight rod
mass = density x length
Velocity for COM
m1v1 + m2v2 + m3v3 / m1 + m2 + m3
Acceleration for COM
m1a1 + m2a2 + m3a3 / m1 + m2 + m3
Moment of inertia
I = mr^2
Moment of inertia of uniform rod with axis on left side
I = 1/3ML^2
Moment of inertia of rectangular plate
I = 1/12 M (a^2 + b^2), a and b are length of plate
Moment of inertia of rectangular plate with axis about its edge
I = 1/12 M a^2
Radius of gyration
I = mk^2, k = radius of gyration or I = Ak^2
Moment of inertia of uniform rod with axis at centre
I = 1/3 M (L^2 - 3Lh + 3h^2); L= total length of rod, h = Distance from axis to end
Moment of inertia of a solid sphere
I = 2/5 MR^2
