With the aid of a string, a gyroscope is accelerated from rest to 32 rad/s in 0.40 s. What is its angular acceleration in rad/s2? How many revolutions does it go through in the process?

Explanation:

We have equation of motion v = u + at

     Initial angular velocity, u = 0 rad/s

     Final angular velocity, v = 32 rad/s    

     Time, t = 0.40 s

     Substituting

                      v = u + at  

                      32 = 0 + a x 0.40

                      a = 80 rad/s²

     Angular acceleration is 80 rad/s²

  We have equation of motion s = ut + 0.5 at²

        Initial angular velocity, u = 0 rad/s

        Angular acceleration, a = 80 rad/s²

        Time, t = 0.4 s      

     Substituting

                      s = ut + 0.5 at²

                      s = 0 x 0.4 + 0.5 x 80 x 0.4²

                      s = 6.4 rad

      Angular displacement  = 6.4 rad

Number of revolutions undergone is 1.02

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.

this is an example of "committed" time.

committed time, as contracted time, takes need over essential and available time since it is seen as profitable work. it alludes to the time allotted to keep up a home and family. at the point when a man is commuting using committed time this individual may feel that the drive is an obligation to family, for example, strolling youngsters to class or driving a mate to work. contracted and committed time clients may feel that their commute could really compare to the commute of important or leisure time clients on the grounds that their commute is profitable work. in this manner, they might be more disposed to pick a mechanized method of movement.