Engineering mechanics

Unit – V

Questions

Question 1) Difference between Perpendicular Axis Theorem And Parallel Axis Theorem

Answer 1)

Question 2) Explain dynamics?

Answer 2)

 Dynamics is the branch of mechanics that deals with the motion of the particle or a rigid body. In other words, dynamics deals with the accelerated motion of a body. Analysis in dynamics involves motion. Dynamics can be sub-divided into two parts:

1. Kinematics

Kinematics is the branch of mechanics or simply a part of dynamic analysis which deals with the study or analysis of the motion of the body without considering the forces that causes this motion.

Hence Kinematics only analyses the geometry of the particle or rigid body.

2.     Kinetics

Kinetics is the branch of mechanics or simply a part of dynamic analysis which deals with the study of motion of the body by considering the forces that causes this motion.

In other words, kinematics relates with the forces acting on the moving body.

Dynamics can be also classified on the basis of the body under study.

1. Particle dynamics

Particle is nothing but a point body or a body who does not have any size and shape. Analysis of a particle in motion is referred to as particle dynamics

2.     Rigid body dynamics

Rigid body is a body who does not change its shape and size when subjected to various forces and couples. Analysis of rigid body is referred to as rigid body dynamics

Question 3) Differences between Moment Of Inertia and Polar Moment of Inertia?

Answer 3)

While the moment of inertia and polar moment of inertia sound similar they are two different quantities for measuring different properties of certain objects. We will look at a few differences below.

Question 4) from a uniform circular disc of radius R and mass 9 M, a small disc of radius R/3 is removed as shown in the figure. Calculate the moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through the centre of the disc.

Answer 4)

Solution:

The moment of inertia of removed part abut the axis passing through the centre of mass and perpendicular to the plane of the disc = Icm + md2

= [m × (R/3)2]/2 + m × [4R2/9] = mR2/2

Therefore, the moment of inertia of the remaining portion = moment of inertia of the complete disc – moment of inertia of the removed portion

= 9mR2/2 – mR2/2 = 8mR2/2

Therefore, the moment of inertia of the remaining portion (I remaining) = 4mR2.

Question 5) Moment Two balls connected by a rod, as shown in the figure below (Ignore rod’s mass). Mass of ball X is 700 grams and the mass of ball Y is 500 grams. What is the moment of inertia of the system about AB?

Answer 5)

Given

The rotation axis is AB

mX = 700 grams = 0.7 kg

mY = 500 grams = 0.5 kg

rX = 10cm = 0.1m

rY = 40cm = 0.4m

Solution: 

I = mX rX2 + mY rY2

I = (0.7)× (0.1)2 + (0.5)× (0.4)2

I = 7 × 10-3 + 0.08

I = 0.087 kg m2

Moment of inertia of the system is 0.087 kg m2

Question 6) two balls connected by a rod as shown in the figure below (Ignore rod’s mass). What is the moment of inertia of the system?

Answer 6)

Given

mX = 300 grams = 0.3 kg

mY = 500 grams = 0.5 kg

rX = 0cm = 0m

rY = 30cm = 0.3m

Solution:

I = mX rX2 + mY rY2

I = (0.3)× (0)2 + (0.5)× (0.3)2

I = 0 + 0.045

I = 0.045 kg m2

Moment of inertia of the system is 0.045kg m2

Question 7) The mass of each ball is 200 gram, connected by cord. The length of cord is 80 cm and the width of cord is 40 cm. What is the moment of inertia of the balls about the axis of rotation (Ignore cord’s mass).

Answer 7)

Given

Mass of ball = m1 = m2 = m3 = m4 = 200 gram = 0.2kg

Distance between ball and the axis of rotation (r1) = 40cm = 0.4 m

Distance between ball 2 and the axis of rotation (r2) = 40 cm = 0.4 m

Distance between ball 3 and the axis of rotation (r2) = 40 cm = 0.4 m

Distance between ball 4 and the axis of rotation (r2) = 40 cm = 0.4 m

Solu:

I = m1 r12 + m2 r22 + m3 r32 + m4 r42

I = (0.2) × (0.4)2 + (0.2) × (0.4 m)2 + (0.2) × (0.4)2 + (0.2) × (0.4)2

I = 0.032 + 0.032 + 0.032 + 0.032

I = 0.128 kg m2

Moment of inertia of the balls about the axis o.128 kg m2

Question 8) what is the Difference between Static Friction and Kinetic Friction?

Answer 8)

Question 9) what is the difference between Kinetics and Kinematics?

Answer 9)

Kinetics is focused on understanding the cause of different types of motions of an object such as rotational motion in which the object experiences force or torque. 

Kinematics explains the terms such as acceleration, velocity, and position of objects. The mass of the object is not considered while studying the kinematics.

Question 10) Explain parallel axis theorem?

Answer 10) Parallel Axis Theorem Derivation

Let Ic be the moment of inertia of an axis which is passing through the center of mass (AB from the figure) and I be the moment of inertia about the axis A’B’ at a distance of h.

Consider a particle of mass m at a distance r from the center of gravity of the body.
Then,
Distance from A’B’ = r + h

I = ∑m (r + h)2

I = ∑m (r2 + h2 + 2rh)

I = ∑mr2 + ∑mh2 + ∑2rh

I = Ic + h2∑m + 2h∑mr

I = Ic + Mh2 + 0

I = Ic + Mh2