1. A carousel rotates at a constant angular velocity of 0.2 rad/s. Determine the angle through
which the carousel rotates in 1 minute.
  t
  0.2 rad/s  60s   12 rad
2. The earth rotates around its axis at an angular speed of 7.27 105 rad/s .
a. How long does it take to rotate 6.28 rad?
b. How many seconds are in 1 day?
c. Could you have done part a in your head?
a)
  t  t 



6.28 rad
7.27 105 rad/s
 86400s
b)
 60s/min  60min/hr  24hr/day   86400s/day
c) Yes. 6.28 is about 2 , which is one full rotation. The earth makes 1 full rotation per day.
3. The earth makes 1 full revolution around the sun per year (365 days). What is the earth’s
rotational velocity in rad/s?
  t   


t
6.28 rad
1yr  60s/min  60 min/hr  24 hr/day  365days/yr 
 2 107 rad/s
4. A fan starts from rest. After 3.2 s of constant angular acceleration, the fan turns at a rate of
2628 rad/s.
a. Find the fan’s angular acceleration.
b. Determine the angle through which the fan rotates during this period.
  t   

t
2628 rad/s

3.2s
 820 rad/s 2
1
   t 2
2
1
2
  821.25 rad/s 2   3.2s 
2
 4200 rad