Page 69 - Mechanical Engineer's Data Handbook

58 MECHANICAL ENGINEER'S DATA HANDBOOK

Similar relationships are given for circular motion 2. I .6 Centripetal acceleration
with constant angular acceleration. In practice, accel-
eration may vary with time, in which case analysis is For a mass m rotating at orads-' at radius r:
much more difficult.
Tangential velocity v = ro
2. I .5 Acceleration V2
Centripetal acceleration =-=roz
Linear acceleration r

Symbols used: Centripetal force = mro2 (acting inwards on m)
u = initial velocity Centrifugal force = mro2 (acting outwards on pivot)
v = final velocity
t = time
a = acceleration
x = distance

s s

And:x= vdt; v= adt

Equations of motion:
v=u+at 2. I .7 Newton's laws of motion

x=- (u + u) These state that:
2t
(1) A body remains at rest or continues in a straight
v2 = u2 +2ax line at a constant velocity unless acted upon by an
1
x = ut + Tat 2 external force.
(2) A force applied to a body accelerates the body by
Angular acceleration
an amount which is proportional to the force.
Let: (3) Every action is opposed by an equal and opposite
reaction.
o1 =initial angular velocity
w2 =final angular velocity
t = time 2. I .8 Work, energy and power
O= angle of rotation
a = angular acceleration Kinetic, potential, strain and rotational kinetic energy
are defined and the relationships between work, force
and power are given.
s s Work done W= force x distance = Fx (Nm = J)
s
And: 8= odt: o= adt Work done by variable force W= F dx

Equations of motion:
Work done by torque (7') W= TO
s
w2 = w1 +at where: O =angle of rotation.
Also W= TdO

mu'
Kinetic energy KE = -
2