Question

A wheel rotates with a constant angular acceleration of 3.0 rad/. If the angular speed of the wheel is 2 rad/s at t = 0, through what angular displacement does the wheel rotate in 2 s?

10 rad.
	6 rad.
	15 rad.
	4 rad.
	12 rad.

Based on question number 3, through how many revolutions has the wheel turned during this time interval?  

4 rev.
	3 rev.
	1.6 rev.
	5 rev.
	2 rev.

Based on question number 3, what is the angular speed of the wheel at t = 2 s?  

10 rad/s.
	12 rad/s.
	8 rad/s.
	6 rad/s.
	2 rad/s.

Answer 1

a) As the wheel is rotating with constant angular acceleration , = 3 rad/sec2

at time t =0 , its angular speed = o = 2 rad/sec

to find its angular displacement in 2 seconds , we will use equation of motion in rotational mechanics :

in analogy with S = u t + 1/2 a t2

on substituting the values of time, initial angular speed and angular acceleration , we get

   = 2 2 + 1/2 3 22

   = 10 radians

b) as there is an angle of 2 in one complete revolution

    = 2 *3.14 =6.28 radians is the total angular displacement in one revolution .

at time t = 2 seconds , the angular displacement is 10 radians

hence, the total revolutions , wheel has turned in this time interval = 10/ 6.28

                                                                                                             = 1.6 rev

c)angular speed at time t= 2 seconds is

    = 2 + 3 2

    = 8 radians / sec