A 165-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force would have to be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.600 rev/s in 2.00 s? (State the magnitude of the force.) N

233.3N

Explanation:

Given:

radius 'r'= 1.5m

mass 'm'= 165kg

time 't'=2 sec

angular speed 'ω'= 0.6 rev/s

the magnitude of a torque is given by:

τ = F . r = I . α

where, 'α' is the angular acceleration and  'I' is the rotational inertia

F=  I . α/ r =>[ ( . m . )(2π . ω/t) ]/r

F=[( . 165 . )(2π . 0.6/2)]/1.5

F= 233.3N

the components of a vector are the parts of the vectors that are to each other.

b perpendicular

it is given that trillions of microbes make up to 1% to 3% of the body mass.

let's take average of this percentage: 2%

consider the average mass of the human body as 70 kg.

then, trillions of microbes would have mass  

therefore, 100 trillion micro-organisms would weigh:

this is an approximate value and could change depending on the mass of the human body and percentage of the microbes present in it.

average mass per microorganism =