Mechanical Rate(a.k.a. Motion)

http://www.uhigh.ilstu.edu/tech/PT/

TEKS• TLW knows the laws governing motion (TEKS

5)• TEKS 5.A - Analyze examples of uniform and accelerated

motion – including linear, projectile, & circular

• TEKS 5.B - Generate and interpret graphs describing motion including the use of real-time technology

• TEKS 5.C – Formulate the effects of forces on motion of objects

• TEKS 5.D – Develop and interpret a free-body diagram for force analysis

• TEKS 5.E – Identify and describe motion relative to different frames of reference

Lesson Plan Objectives

• Identify and describe motion relative to different frames 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)

Time interval (t)Speed =

Examples of units to use: m/sec, km/hr, ft/sec, or miles/hr

Average Speed• When speed varies between point A and B

Distance traveled (d)

Time interval (t)

Average Speed

=

d

t

savg = =d2 – d1

t2 –t1

d2 = final distance (df) d1 = initial starting point (di)t2 = final time (tf) t1 = initial time (ti)

Velocity• A vector quantity giving the speed

(magnitude) and direction of travel.

displacement

timeVelocity =

d

tvavg =

Acceleration• Describes the rate of change of an object’s velocity

Velocity change (v)

Time interval (t)

Average

Acceleration =

v

t

aavg = =v2 – v1

t2 –t1

Negative acceleration is called deceleration

v2 = final velocity (vf) v1 = initial velocity (vi)t2 = final time (tf) t1 = initial time (ti)

Projectile Motion

Angular Speed

• Rate of rotational motion.

angular displacement ()

time interval (t) () =

Angular

Speed omega

1 revolution = 360º = 2 radians

radians or revolutions

Angular Acceleration• Ration of the change in angular speed to the

time interval.

Angular speed change ()

Time interval (t)

Angular

Acceleration =

ta = =

2 – 1

t2 –t1

Summary• Speed is a measure of the rate of motion of an object. It is the ratio of

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.