Chapter 1
Kinematics and Statics
Abstract Chapter 1 is devoted to problems based on one and two dimensions.
The use of various kinematical formulae and the sign convention are pointed out.
Problems in statics involve force and torque, centre of mass of various systems and
equilibrium.
1.1 Basic Concepts and Formulae
Motion in One Dimension
The notation used is as follows: u = initial velocity, v = final velocity, a = acceleration, s = displacement, t = time (Table 1.1).
Table 1.1 Kinematical equations
U
V
A
S
t
(i) v = u + at
X
(ii) s = ut + 1/2at 2
X
(iii) v 2 = u 2 + 2as
X
(iv) s =
1
2 (u + v)t
X
In each of the equations u is present. Out of the remaining four quantities only
three are required. The initial direction of motion is taken as positive. Along this
direction u and s and a are taken as positive, t is always positive, v can be positive
or negative. As an example, an object is dropped from a rising balloon. Here, the
parameters for the object will be as follows:
u = initial velocity of the balloon (as seen from the ground)
u = +ve, a = −g. t = +ve, v = +ve or −ve depending on the value of t, s = +ve
or −ve, if s =−ve, then the object is found below the point it was released.
Note that (ii) and (iii) are quadratic. Depending on the value of u, both the
roots may be real or only one may be real or both may be imaginary and therefore
unphysical.
1
Kinematics and Statics
Abstract Chapter 1 is devoted to problems based on one and two dimensions.
The use of various kinematical formulae and the sign convention are pointed out.
Problems in statics involve force and torque, centre of mass of various systems and
equilibrium.
1.1 Basic Concepts and Formulae
Motion in One Dimension
The notation used is as follows: u = initial velocity, v = final velocity, a = acceleration, s = displacement, t = time (Table 1.1).
Table 1.1 Kinematical equations
U
V
A
S
t
(i) v = u + at
X
(ii) s = ut + 1/2at 2
X
(iii) v 2 = u 2 + 2as
X
(iv) s =
1
2 (u + v)t
X
In each of the equations u is present. Out of the remaining four quantities only
three are required. The initial direction of motion is taken as positive. Along this
direction u and s and a are taken as positive, t is always positive, v can be positive
or negative. As an example, an object is dropped from a rising balloon. Here, the
parameters for the object will be as follows:
u = initial velocity of the balloon (as seen from the ground)
u = +ve, a = −g. t = +ve, v = +ve or −ve depending on the value of t, s = +ve
or −ve, if s =−ve, then the object is found below the point it was released.
Note that (ii) and (iii) are quadratic. Depending on the value of u, both the
roots may be real or only one may be real or both may be imaginary and therefore
unphysical.
1