Mechanics of Rigid Bodies

Question 1

What is a rigid body?

Answer 1

A rigid body is a body with an axis of rotation and whose axis is stable.

Question 2

What causes rotational motion?

Answer 2

Torque

Question 3

What is the unit of Torque?

Answer 3

Nm

Question 4

Name one special property of a rigid body.

Answer 4

It can perform both translational and rotational motion.

Question 5

What causes rotational motion?

Answer 5

Torque

Question 6

What is the moment of a vector?

Answer 6

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

Question 7

What is torque?

Answer 7

It refers to the moment of a force.

Question 8

What is angular momentum?

Answer 8

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

Question 9

What is a couple?

Answer 9

A couple refers to two equal and opposite forces whose lines of action do not coincide. These forces usually bring about a turning effect.

Question 10

When is a rigid body said to be in equilibrium?

Answer 10

If the resultant force acting on it is zero. That means that it either remains at rest or in motion with constant velocity.

Question 11

What is the condition for translational equilibrium?

Answer 11

When a body remains at rest or in motion with constant velocity

Question 12

What is the centre of mass?

Answer 12

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.

Question 13

What is the COM of a 1-dimensional body?

Answer 13

It is the point at which it balances.

Question 14

What is the COM of a 2-dimensional body?

Answer 14

It is the point at which it balances.

Question 15

What is the COM of a 3-dimensional body?

Answer 15

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

Question 16

What is the centre of gravity of a body?

Answer 16

It is the point where the resultant force of attraction is concentrated, i.e. where the weight is concentrated.

Question 17

State the parallel axis theorem

Answer 17

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.

Question 18

What is the radius of gyration?

Answer 18

It is the mass moment of inertia of a body about a specific axis.

Question 19

Torque

Answer 19

Fr or Frsin@

Question 20

Angular momentum

Answer 20

rP or rmv or mvr

Question 21

COM

Answer 21

m1x1 + m2x2 + m3x3 / m1 + m2 + m3

Question 22

COM for thin straight rod

Answer 22

mass = density x length

Question 23

Velocity for COM

Answer 23

m1v1 + m2v2 + m3v3 / m1 + m2 + m3

Question 24

Acceleration for COM

Answer 24

m1a1 + m2a2 + m3a3 / m1 + m2 + m3

Question 25

Moment of inertia

Answer 25

I = mr^2

Question 26

Moment of inertia of uniform rod with axis on left side

Answer 26

I = 1/3ML^2

Question 27

Moment of inertia of rectangular plate

Answer 27

I = 1/12 M (a^2 + b^2), a and b are length of plate

Question 28

Moment of inertia of rectangular plate with axis about its edge

Answer 28

I = 1/12 M a^2

Question 29

Radius of gyration

Answer 29

I = mk^2, k = radius of gyration or I = Ak^2

Question 30

Moment of inertia of uniform rod with axis at centre

Answer 30

I = 1/3 M (L^2 - 3Lh + 3h^2); L= total length of rod, h = Distance from axis to end

Question 31

Moment of inertia of a solid sphere

Answer 31

I = 2/5 MR^2