With the aid of a string, a gyroscope is accelerated from rest to 16 rad/s in 0.40 s. What is its angular acceleration in rad/s2? Approximately how many revolutions does it go through in the process?

Explanation:

Given that,

A gyroscope accelerated from rest

Initial angular speed ωi = 0

The gyroscope accelerated to

ωf = 16rad/s

time taken t = 0.4s

A. What is it's angular acceleration α?

Using equation of circular motion

ωf = ωi + αt

16 = 0 + 0.4α

16 = 0.4α

then, α = 16 / 0.4

α = 40rad/s2

The angular acceleration is 40rad/s².

b. Revolution θ?

Using circular motion equation

ωf² = ωi² + 2α∆θ

16² = 0² + 2×40∆θ

256 = 0 + 80∆θ

256 = 80∆θ

∆θ = 256 / 80

∆θ = 3.2 rad.

θf - θi = 3.2rad

The initial revolution Is zero, since it starts from rest

θ = 3.2rad

We know that, 1 rev = 2πrad

Then, θ = 3.2 rad × 1rev/2πrad

θ = 0.51 revolution

θ ≈ 0.5 revolution

So, gyroscope makes an approximately 0.5 revolution in 0.4 seconds

.) the observation by semmelweis that more mothers died of childbed fever when their doctors also worked in the morgue

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s