Chap 3 – Sec 1

Rate in Mechanical Systems

Objectives

• Define speed, velocity & acceleration.• Explain the difference between speed &

velocity.• Explain the difference between velocity

and acceleration.• Define angular speed & angular

acceleration.• Solve problems in linear & angular motion.

Speed

• Speed equals the distance traveled divided by the time it took to travel it.

• Speed = distance / time = d/t• Average speed is the total distance

traveled divided by the total time.• Instantaneous speed is the speed at a

given instant in time. Ex – speedometer reading.

Velocity

• Velocity is a vector quantity. It has a direction & magnitude.

• The magnitude of the velocity vector is speed.

• Example – 50 mph is a speed. 50 mph due north is a vector.

Acceleration

• Acceleration is the change in velocity divided by the change in time, a = v / t

• Any change in the velocity vector is an acceleration.

• Since velocity is a vector, a change in the direction of the vector is an acceleration.

• A car has three accelerators; gas pedal, brake & steering wheel.

Units

• Velocity (speed) – English – ft/s, mph; SI – m/s, kph

• Acceleration – ft/s2 ; SI – m/s2

Angular velocity

• Angular velocity is the change in angle over change in time, =/t

• Units are radians/second; rad/s• Sometimes expressed in revolutions per

minute (RPM).

Angular acceleration

• Angular acceleration is the change in angular velocity over time, = /t.

• Units are rad/s2.

Graphing SpeedDistance - time graph

Series 1

f(x)=2*x+0; R²=1

1 2 3 4 5 6 7 8 9

1

2

3

4

5

6

7

8

9

time (s)

distance (m)

On a distance – time graph:

The slope of the graph is the speed.

Slope = rise / run

Graphing SpeedDistance - time graph

Series 1

f(x)=2*x+0; R²=1

1 2 3 4 5 6 7 8 9

1

2

3

4

5

6

7

8

9

time (s)

distance (m)

Speed = slope

• Slope = rise / run• Rise = 8 – 2 = 6• Run = 4 – 1 = 3• Speed = 6/3 = 2 m/s

Velocity time graphVelocity - time graph

Series 1

f(x)=3*x+0; R²=1

1 2 3 4 5 6 7 8 9

2

4

6

8

10

12

time (s)

speed (m/s)

In a velocity – time graph

Slope = acceleration

Velocity time graphVelocity - time graph

Series 1

f(x)=3*x+0; R²=1

1 2 3 4 5 6 7 8 9

2

4

6

8

10

12

time (s)

speed (m/s)

Acceleration = slope

• Slope = rise / run• Rise = 12 – 3 = 9• Run = 4 – 1 = 3• Acceleration = 9/3 = 3 m/s/s = 3 m/s2

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

is distance traveled divided by time. Speed is a scalar quantity.

• Velocity is displacement divided by time. Velocity is a vector quantity. The magnitude of the velocity vector is speed.

• Acceleration is the rate of change of an object’s velocity. It is velocity divided by time.

• Angular speed is the measure of an object’s rotational motion. It is the change in angle divided by time.

• Angular acceleration is the rate of change of an object’s angular velocity. It is angular velocity divided by time.