Mechanical Rate
(a.k.a. Motion)
http://www.uhigh.ilstu.edu/tech/PT/
TEKS
• TLW knows the laws governing motion
(TEKS 7)
• TEKS 7.A - Generate and interpret relevant equations
using graphs and charts for one- and two-dimensional
motion
• i.
One dimensional equations for: displacement, distance,
speed, velocity, average velocity, acceleration, and average
acceleration
• ii.
Two-dimensional equations for projectile and circular
motion
• iii. Using and describing vector forces and resolution
TEKS
• TLW knows the laws governing motion
(TEKS 7)
• TEKS 7.B – Describe and calculate the effects of forces
on motion of objects including law of inertia, impulse,
and conservation of momentum
• TEKS 7.C – Develop and interpret a free-body diagram
• TEKS 7.D – Identify and describe motion relative to
different frames of reference
Lesson Plan Objectives
• Identify and describe motion relative to different frames
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of reference – such as heights and orbits
Use real-time technology (photo-gates, ramps, stop
watchers, etc.) in hands-on labs
Prepare and interpret graphs from data collected on linear,
projectile, and circular motion
Define Speed, velocity, and acceleration.
Explain the difference between speed and velocity.
Explain the difference between velocity and acceleration.
Use speed, velocity, and acceleration to solve problems
involving linear (one-dimensional) motion.
Lesson Plan Objectives
• Use speed, velocity, and acceleration to
solve problems involving projectile motion
• Define angular speed and angular
acceleration.
• Use angular speed and angular acceleration
to solve problems involving rotational
motion.
• Create and use free-body diagrams to
analyze force scenarios
Speed
• Speed is the ratio between the distance traveled
and the elapsed time. (scalar quantity)
Distance traveled (d)
Speed =
Time interval (t)
Examples of units to use: m/sec, km/hr, ft/sec, or miles/hr
Average Speed
• When speed varies between point A and B
Average Distance traveled (d)
=
Speed
Time interval (t)
savg
=
d
t
d2 = final distance (df)
t2 = final time (tf)
=
d2 – d1
t2 –t1
d1 = initial starting point (di)
t1 = initial time (ti)
Velocity
• A vector quantity giving the speed
(magnitude) and direction of travel.
distance
Velocity =
time
vavg
d
=
t
Acceleration
• Describes the rate of change of an object’s velocity
Average
Velocity
change
(v)
=
Acceleration
Time interval (t)
aavg
v
=
v2 = final velocity (vf)
t2 = final time (tf)
t
v2 – v1
=
t2 –t1
v1 = initial velocity (vi)
t1 = initial time (ti)
Negative acceleration is called deceleration
Free Fall
• Definition – the movement of an object in response to
gravitation attraction
• As an object falls towards Earth it will accelerate at a
constant rate of 9.8 m/s2 – regardless of mass ( g =
9.8 m/s2)
• It is common to neglect air resistance in high school
curriculum… but it does play a part in real life
• Downward acceleration will be positive, upward will
be represented by a negative. …. Likewise, upward
velocity will be negative and upward direction will be
negative.
Free Fall
• Displacement of falling object =
Δd = vinitialΔt + (1/2)g Δt2
• Final velocity of falling object =
vfinal2 = vinitial2 + 2g Δd
• OR Final velocity of falling object =
vfinal = vinitial + g Δt
Free Fall
• Time for object to reach Earth =
Δt = vfinal - vinitial
g
• OR Time for object to reach Earth =
Δt =
2 Δd
g
Projectile Motion
• A projectile is any object upon which the
only force is gravity
• Projectiles travel with a parabolic trajectory
due to the influence of gravity
• There are no horizontal forces acting upon
projectiles, and thus no horizontal
acceleration
Projectile Motion
• Projectiles always maintain a constant
horizontal velocity (neglecting air resistance)
• Projectiles always experience a constant vertical
acceleration of 9.8 m/s2 downward (neglecting
air resistance).
• Horizontal and vertical motion are completely
independent of each other. (i. e. – there are
horizontal and vertical components to velocity)
Projectile Motion
• For an object beginning and ending at the same
height it takes the same amount of time to reach
highest point as it does to return to original
position
• Objects dropped from a moving vehicle have
the same velocity as that vehicle
Projectile Motion
• horizontal distance (dx) in meters =
vxt
• vertical distance (dy) in meters =
vy∆t + 1/2g∆t2
• vertical distance (dy) at an angle in meters =
vy(sin θ) ∆t + 1/2g∆t2
Projectile Motion
• angular range (R) in meters = vi2sin 2 θ
g
• hang time (t) in seconds = 2vy(sin θ)
g
Angular Speed
• Rate of rotational motion.
Angular
() =
Speed
radians or
revolutions
angular displacement ()
time interval (t)
omega
1 revolution = 360º = 2 radians
Angular Acceleration
• Ration of the change in angular speed to the
time interval.
Angular speed change ()
Angular
=
Acceleration
Time interval (t)
a =

t
2 – 1
=
t2 –t1
Summary
• Speed is a measure of the rate of motion of an object. It is the ratio of
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distance traveled to the time interval. Speed is a scalar quantity.
Velocity is the ratio of displacement to the time interval. Velocity and
displacement are vector quantities. Speed is the magnitude of
velocity.
Acceleration is a measure of the rate of change of an object’s velocity.
It is the ratio of change in velocity to the time interval.
Angular speed is a measure of the rate of rotational motion of an
object. It is the ratio of angular displacement to time interval.
Angular acceleration is a measure of the rate of change of an object’s
angular speed. It is the ratio of change in angular speed to the time
interval.