Lesson 4.1 Homework Solutions
1.
Express the following angles in radians. Give your answer as
multiples of
π
.
(i)
30
o
, (ii) 45
o
, (iii) 53
o
, (iv) 90
o
, (v) 150
o
, (vi) 420
o
.
5
7
( )
( )
(
) 0.29
(
)
( )
(
)
6
4
2
6
3
i
ii
iii
iv
v
vi
π
π
π
π
π
π
2.
What is the angular velocity of the earth (i) in its orbit around the sun,
(ii) about its axis?
(
i)
The earth goes round the sun in 365 days.
7
1
2 ,
365
24
60
60
2
365
24
60
60
1.99
10
rad s
t
s
t
θ
π
θ
π
ω
−
−
=
=
×
×
×
=
=
=
×
×
×
×
(ii)
The earth rotates completely once about its axis in 24 h
5
1
2 ,
24
60
60
2
24
60
6
7.3
1
0
0
t
s
r
s
t
ad
θ
π
θ
π
ω
−
−
=
=
×
×
=
=
=
×
×
×
3.
A CDROM in a computer rotates at 700 rpm. How long will it take
for the disc to make one revolution?
The time taken for 700 revolutions = 1 minute = 60 s
The time taken for one revolution is:
1
60
700 revolutio
0.086
ns
s re
l
s
vo
−
=
=
4.
A turn table set for 45 rpm is turned on and reached its operating
speed in 1.25 s. What is the average angular acceleration of the turn
table?

2
1
45
2
0,
45 rpm
rad s
,
1.25
60
45
2
60
1
.
2
7
5
3 7
.
i
f
f
i
t
s
t
rad s
π
ω
ω
ω
ω
π
α
−
×
=
=
=
=
−
×
=
=
=
×
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