Unit 3 - Rate
Rate Overview / Rate in the
Mechanical System
Rate Overview
1. What is Rate?
- how far, how often or how much
something moves in a period of time
2. Generally, how do we calculate rate?
- Rate = Displacement Quantity
Elapsed Time
- each system has a different
displacement quantity
Rate Overview
3. What is the displacement quantity in the
mechanical system?
- there are two, namely:
linear
distance, units foot or meter
rotational
angular distance, units radians or
revolutions
Rate Overview
4. What is the displacement quantity in
the fluid system?
- volume or a mass
- volume:
cubic inch (in3) or
cubic centimeter (cm3 or ccs)
- mass - kilogram
Rate Overview
5. What is the displacement quantity in
the electrical system?
- charge in units of coulombs
6. What is the displacement quantity in
the thermal system?
- heat energy in units of calories
Rate in Mechanical System
1. What does rate measure in the
mechanical system?
- speed or velocity
2. What does speed tell us?
- how fast an object moves
Rate in the Mechanical System
3. How does speed
differ from velocity?
- speed tells you
how fast an object is
moving
- velocity tells you
both the speed of an
object and its
direction
Rate in the Mechanical System
4. Which is a scalar
quantity – speed or
velocity?
- speed is scalar
- velocity is a vector
Rate in Mechanical System
5. What 2 factors
must you know
to calculate an
object’s speed?
- distance moved
- elapsed time
Rate in the Mechanical System
6. How does linear speed
differ from angular
speed?
- linear speed is the rate
of motion in a straight
line
- angular speed is the
rate of motion through
an angle
Rate in the Mechanical System
7. How do we calculate linear speed (v)?
- speed equals distance (d) divided by
elapsed time (t)
-v=d
t
Rate in the Mechanical System
8. What is the correct
unit for linear speed?
- there is not one
correct unit for speed
- the unit depends on
what units are given
for distance and time
Rate in the Mechanical System
9. What are some
common English units
for speed?
- ft/sec (standard)
- mi/hr or mph
- 1 mi/hr = 1.47 ft/sec
Rate in the Mechanical System
10. What are some
common SI units for
speed?
- m/s (standard)
- km/hr
- 1 km/hr = 0.278 m/s
Rate in the Mechanical System
11. Example – An automobile travels 250 ft
east in 10 seconds at a constant speed.
What is the speed of the car? What is the
velocity of the car?
-v=d
d = 250 ft
t
t = 10 seconds
- v = 250 ft v = 25 ft/s – (speed)
10 s v = 25 ft/s east – (velocity)
Rate in the Mechanical System
12. What is the difference between
instantaneous speed and average speed?
- average speed is the determined over a
period of time
- instantaneous speed is the speed at a
certain time (ex. speedometer reading)
- we calculate average speed rather than
instantaneous speed
Rate in the Mechanical System
13. What is acceleration?
- change in the rate of
speed or velocity
14. What are three ways an
object can accelerate?
- speed up, slow down,
change direction
Rate in the Mechanical System
15. How do you calculate acceleration?
a = vf – vi
t
vf – final speed
vi – initial speed
t - time
Rate in the Mechanical System
16. What are some English common units for
acceleration?
- ft/s2 (standard)
- mi/hr2
17. What are some SI common units for
acceleration?
- m/s2 (standard)
- km/hr2
Rate in the Mechanical System
18. Example – A pilot increases the takeoff
speed of a jet plane from 15 ft/sec to 205
ft/sec in 50 seconds. What is the
acceleration of the aircraft?
a = vf – vi
t
a = 205 ft/s – 15 ft/s
50 s
a= 3.8 ft/s2
Rate in Mechanical System

Example – Dragsters
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What is the accel’n
of a dragster that
covers ¼ mile in 5
seconds with a final
speed of 300 mph?
a = (vf – vo)/t
a = (300*1.47-0)/5
a = 88.2 ft/s2
(2.75 “g”)
Rate in the Mechanical System
19. Can acceleration
have a negative
value?
- yes, it occurs when
an object is slowing
down , also known
as “deceleration”
Graphing Rate Changes
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Exercise
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
On graph paper, plot
the ordered pairs of
velocity and time and
join the points
The slope of the line
segments represents
the change of
velocity per unit
time, or
ACCELERATION
Rate in the Mechanical System
20. How do you measure rotational speeds?
- angular speed
- - Greek letter “omega”
- angular speed is measured in
revolutions per minute (rpm), or
radians per second
Rate in the Mechanical System
21. How do you calculate angular speed?
- angular speed = angular displacement
time
- =
t
- = revolutions or radians
- t = time in minutes or seconds
Rate in the Mechanical System
23. Example – The dish of a weather radar
antenna system completes 160 revolutions in
one hour. Find the angular speed in rpm.
- =
t
given hours, must convert
to minutes
-
= 160 revolutions
60 minutes
= 2.67 rpm
Rate in the Mechanical System
24. What does a positive
angular speed mean?
- the object is rotating
clockwise (cw)
25. What does a negative
angular speed mean?
- the object is rotating
counterclockwise (ccw)
Rate in the Mechanical System
26. How does angular acceleration differ
from linear acceleration?
- the Greek letter alpha ( ) is used to
represent angular acceleration
- =( fo)/t
- units of radians/sec2
Example 3-E