PHYSICS

(l05 N 2
) · (0.6 ·W- 2 m ) . (0.12.10- 4 m 2)
m
(9.8 ~). (6 ·W- 2 m )
c
3.2.5. Work and Energy
The work done by a constant force is defined as the product of
the component of the force in the direction of the displacement
and the magnitude of the displacement:
A = F . s = (Fcos 8) s (3.15)
where Fcosq is the component of F in the direction of S . Work
is a scalar quantity and equation 3.15 is the scalar product of the
two vectors F and s .
The SI unit of work is the joule (J = N· m).
The product of one half the mass (m) and the square of the
speed (V) is defined as the kinetic energy of a particle:
1
E k: = -mV 2 (3.16)
2
Potential energy is accumulated in a system as a result of
previous work being done.
For instances, the gravitational potential energy near the
Earth's surface is:
E p
= mgh (3.17)
where m is the mass of the particle and h the displacement.
The elastic potential energy, such as that stored in a spring, is:
E p = '!"/a 2 (3.18)
2
where k is the force constant of the spring and x the displacement.
Animal Extremes!
The smallest bird is the bee hummingbird (Trochi/idae) ­
1.6 g.
3.3. CIRCULAR MOTION
3.3.1. Kinematics of Rotational Motion
If a particle of mass m is traveling in a circular path of radius r
with a tangential velocity of V, the average angular velocity « to>
is the number of radians swept out by the radius in I second:
!18
=- (3.19)
N
where t18 = 8 - 2
8 J
equals the angular displacement.
In analogy to linear velocity, the instantaneous angular velocity
(w) is defined as the limit of the ratio in equation 3.19 as (M)
approaches zero, or:
. t:>e de
w = lim -=- (3.20)
~HO t:>t dt
Angular velocity has units of rad/s or lis, since radians are
not dimensional.
The averaged angular acceleration «f3» of a rotating body is
defined as the ratio of the change in the angular velocity to the
time interval (M):
t:> ta
< f3 > = M (3.21)
In analogy to linear acceleration, the instantaneous angular
acceleration (f3) is defined as the limit of the ratio
· t:>w doi
f3 = 1Im--=- (3.22)
M--.O t:>t dt
Angular acceleration has units of radts' or Its'.
The tangential velocity (V) of a point on a rotating rigid body
equals the distance of that point from the axis multi plied by the
angular velocity, or:
V= rw. (3.23)
The largest animal is blue wale (Belaenoptera musculus) _
190 tons eS!!Jnated weight;
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