1.
A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its angular velocity in
rad/s.

2500 rpm is the angular velocity in revolutions per minute. Convert this in rad/s:
1
min
2
rad
 rev





2
2500

2
.
6
x
10
rad
/
s


 
 
min
60
s
1
rev


 
 
2.
The blades in a blender rotate at a rate of 6500 rpm. When the motor is turned off during
operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades
slow down (in rad/s2)?



 
 
i 6500
rpm
6500

681
rad
/
s

 
 

rev
1
min
2
rad
60
s
1
rev
 min





f  0
(rest)
Angular acceleration is the time rate of change in angular velocity:


0

681
rad
/
s




2
.
3
x
10
rad
/
s

t
3
.
0
s
2
3.
2
A rotating merry-go-round makes one complete revolution in 4.0 s. What is the linear
speed of a child seated 1.2 m from the center?
1
rev
2

rad



 

1
.
57
rad
/
s

4
.
0
s1
rev






v

r
1
.
2
m
1
.
57
rad
/
s

1
.
8
m
/
s

Or:
2 1.2m in 1 revolution

/4

1
.
2
m
.
0
s

1
.
8
m
/s
Linear speed = distance/time = 2
A child seated 1.2 m from the center would travel
4.
A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How
far will a point in the edge of the wheel have travelled in this time?



 

i 240
rpm
240

 


rev
1
min
2
rad


25
.
1
rad
/
s

60
s
1
rev
 min






1
min
2
rad
 rev





f 360
rpm
360

37
.
7
rad
/
s

 
 



60
s
1
rev
 min






37
.
7
rad
/
s

25
.
1
rad
/
s
2



1
.
94
rad
/
s

t
6
.
5
s
1
1 22
2
2










t

t

25
.
1
rad
/
s
6
.
5
s

1
.
94
rad
/
s
6
.
5
s

20
ra
i
2
2



During this time, a point on the edge of the wheel would have travelled
0
.33
m

204

34
m


 2
*Remember that for each 1 radian of angular displacement, a point travels a
distance equal to r
5.
A cooling fan is turned off when it is running at 850 rev/min. It turns 1500 revolutions
before it comes to a stop. How long did it take the fan to come to a complete stop?
1
min
2

rad
 rev






850
rev
/min
850

89
rad
/
s

 
 

i
60
s
1
rev
 min





f  0
(rest)
2
 
2



i 
2
f





0

89
rad
/
s




0
.
42
rad
/
s
2

rad
2

2




1500
rev
 
2 2
f
i
2
1
rev


0

89
rad
/
s
t


212
s
2

0
.
42
rad
/
s


2