Precalculus A Worksheet 09-02
Angular and Linear Velocity II
Section 5.1
Name _____________________
Date _________ Period ______
Please answer the following questions. Be sure to include the appropriate units.
1)
Find the distance, s, of the arc traveled by the point, p, on a rotating object if   15
radians per second, r  5 feet, and t  1 minute.
r
 s
r
p
2)
Find the angular velocity associated with 5.8 rpm.
3)
Find v if r  1 foot and a point rotates at 20 rpm.
4)
The Earth rotates through one complete revolution every 24 hours. Since the axis of
rotation is perpendicular to the equator, if a person was standing on the equator it would
be like a person standing on the edge of a disk that is rotating once every 24 hours.
a) Find the angular velocity (per hour) of a person that is standing on the equator.
b) Assuming the radius of the earth is 4000 miles, what is the linear velocity of a
person standing on the equator?
5)
A boy is twirling a model airplane on a string 5 feet long. If the plane takes 2 seconds to
make one revolution, how far does the tip of the string travel in 2 minutes?
6)
A power lawnmower has a blade that is 2 feet long. If the tip of the blade is traveling
at 1100 feet per second, what is the rpm of the blade?
7)
The original Ferris Wheel (built in Chicago for the 1893
Columbian Exhibition) was 264 feet in diameter and took
nine minutes to complete one revolution. Find the linear
velocity of a person riding on the wheel.
8)
The Colossus Ferris Wheel (built in St. Louis in 1986) is 165 feet in
diameter. A brochure that gives some statistics about the Colossus
indicates that the wheel rotates at 1.5 rpm, and also that a rider on the
wheel travels at 10 mph. Show why these two numbers cannot be correct.
9)
A woman rides a bicycle for 1 hour and travels 16 km. Find the angular
velocity of the wheel if the radius is 30 cm.
10) A pendulum on a clock swings through an angle of 20 each second. If the
pendulum is 40 inches long, how far does its tip move each second?
Analysis A Worksheet 09-02
Angular and Linear Velocity II
Section 5.1
Answer Key
Please answer the following questions. Be sure to include the appropriate units.
1)
Find the distance, s, of the arc traveled by the point, p, on a rotating object if   15
radians per second, r  5 feet, and t  1 minute.
15 radians
 60 seconds   900 radians per minute
second
s  r   5  900   4500 feet

2)
r
 s
r
p
Find the angular velocity associated with 5.8 rpm.
  5.8 2   11.6  36.44 radians per minute
3)
Find v if r  1 foot and a point rotates at 20 rpm.
  20 2   40 radians per minute
v  r   1  40   125.66 feet per minute
4)
The Earth rotates through one complete revolution every 24 hours. Since the axis of
rotation is perpendicular to the equator, if a person was standing on the equator it would
be like a person standing on the edge of a disk that is rotating once every 24 hours.
a) Find the angular velocity (per hour) of a person that is standing on the equator.

2


 0.26 radians per hour
24 12
b) Assuming the radius of the earth is 4000 miles, what is the linear velocity of a
person standing on the equator?

v  r   4000    1047.2 miles per hour
 12 
5)
A boy is twirling a model airplane on a string 5 feet long. If the plane takes 2 seconds to
make one revolution, how far does the tip of the string travel in 2 minutes?
  30 2   60 radians per minute
  60 2 minutes   120
s  5 120   600  1, 884.96 feet
6)
A power lawnmower has a blade that is 2 feet long. If the tip of the blade is traveling
at 1100 feet per second, what is the rpm of the blade?
v  r
1100 f/s  1
  1100 radians per second  66000 radians per minute  10,504 rpm
7)
The original Ferris Wheel (built in Chicago for the 1893
Columbian Exhibition) was 264 feet in diameter and took
nine minutes to complete one revolution. Find the linear
velocity of a person riding on the wheel.
2
radians per minute
9
 2  88
v  r   132 
 92.15 feet per minute

3
 9 

8)
The Colossus Ferris Wheel (built in St. Louis in 1986) is 165 feet in
diameter. A brochure that gives some statistics about the Colossus
indicates that the wheel rotates at 1.5 rpm, and also that a rider on the
wheel travels at 10 mph. Show why these two numbers cannot be correct.
  1.5 2   3 radians per minute  180 radians per hour
v  82.5 180   14,850 
44, 652.65 feet per hour
 8.84 mph
5,280 feet per mile
Either the wheel rotates faster than stated, or else has a slower linear velocity
9)
A woman rides a bicycle for 1 hour and travels 16 km. Find the angular
velocity of the wheel if the radius is 30 cm.
v  r
16 km per hour  30 cm  
16, 000 meters per hour  .3 meters  

16, 000
 53,333 radians per hour
.3
10) A pendulum on a clock swings through an angle of 20 each second. If the
pendulum is 40 inches long, how far does its tip move each second?
20 2 


radians per second
360 18 9
   40
v  40   
 13.96 inches per second
9
9
