Linear and Angular Velocity Lesson

Linear Speed

Trigonometry

Ma'am Michelle M. Villanueva

Multiple Choice

If a car travels 400 m in 20 seconds, how fast is it going?

• 20 m/s

• 0.05 m/s

Multiple Choice

If you move 50 meters in 10 seconds, what is your speed?

• 5 m/s

• 0.2 m/s

Multiple Choice

You arrived in my class 45 seconds after leaving the Registrar’s Office which is 90 meters away. How fast did you travel?

• 0.5 m/s

• 2 m/s

“Drive Me Safely”

Use the “Race Track Interactive” to drive the “car” and avoid crashing from the corners of the “race track”. Utilize the “arrow keys” to move the car from the starting point up to the finish line. 

https://www.physicsclassroom.com/Physics-Interactives/Circular-and-Satellite-Motion/Race-Track/Race-Track-Interactive

What is It

• “How fast is the motorcycle traveling?” This question might be answered with “60 kilometers per hour”, or “17 meters per second”. These answers indicate the motorcycle’s linear speed, a measure of how fast the motorcycle will travel in one unit of time.

• Recall that (see Figure 1),
                    

   $s=r\theta$  

What is It

• Recall that (see Figure 1),                    $s=r\theta$ 

•  If we divide Equation 1 by , we get   $\frac{s}{t}=\frac{r\theta}{t}$  
  

• The expression  $\frac{s}{t}$  , is the change in arc length per unit change in time. We call this linear speed of a point on a circle and denote it by  $v$ .  $v=\frac{s}{t}$  

What is It

• If  is the radius of a circle and  is the length of the arc on the circle, then the linear speed  and angular speed , respectively, are given by:  $v=\frac{s}{t}=r\cdot\frac{\theta}{t}=r\omega$  

Multiple Choice

Example #1

A point on a circle travels  in  $$7$$   cm in  $$2$$  sec. Find the linear velocity of the point.

• 3.5 cm/s

• 14 cm/s

• 0.29 cm/s

Multiple Choice

Example #2

Find the distance $$s$$  covered by a point moving with linear velocity $$v=65\$$  mi./h and  $$t=0.5$$ h.

• 130 mi.

• 32.5 mi.
  

Multiple Choice

Example #3

The pulley has a radius of  $$14$$ cm. Suppose it takes $$15$$ sec. for $$60$$ cm. of belt to go around. Find the linear speed of the belt in cm per sec. 

• 0.25 cm/s

• 4 cm/s

Multiple Choice

Example #4

A railroad track is laid along the arc of a circle of radius 1500 ft. The circular part of the track subtends a central angle of 30°. How long (in seconds) will it take a point on the front of a train traveling 15mi per hour to go around this portion of the track?

• 9 h

• 0.0099 h

Multiple Choice

Example #5

A bicycle is traveling uniformly at 15 kilometers per hour. Its wheels have a 622 mm diameter. Find the number of revolutions made by the wheel in 20 seconds.

• 2.56 rev

• 2.65 rev

Multiple Choice

Example #6

The linear speed of a point on the rim of a 30-m wheel is 90 m per second. Find the angular speed of the wheel.

• 0.17 rad/s

• 6 rad/s

Multiple Choice

Example #7

The linear speed of a point on the rim of a 30-m wheel is 90 m per second. If the angular speed of the wheel is 6 rad/s, find the number of radians which the point generates in 15 seconds.

• 90 rad

• 0.4 rad

Open Ended

What I Have Learned

______1________ is a measure of how ___2________ the object will travel in __3____ unit of ___4____. The linear speed can be expressed by the product of radius and ______5______ in radians per unit time.

Open Ended

Complete the crossword puzzle.

Down:

1. It is the rate of change in angle measure of a unit of time.

3. It is the process of moving or changing place or position.

4. It refers to how fast an object is moving.

Across:

2. It is the circular motion of an object around its center.

5. It is the rate of change in arc length over a unit of time.