"A grinding wheel with a moment of inertia of 2.0 kg-m2 has a 2.5 N-m torque applied to it. What is its final kinetic energy 10 seconds after starting from rest?"

Ek = 156.25 J

Explanation:

Given:-

- The moment of inertia of the grinding wheel I = 2.0 kg-m2

- The torque applied T = 2.5 N-m

Find:-

What is its final kinetic energy 10 seconds after starting from rest?"

Solution:-

- The relationship between applied torque and the angular acceleration α of the grinding wheel is can be expressed as:

                                       T = I*α

- Solve for α , using the given data:

                                       2.5 = 2.0*α

                                       α = 1.25 rad / s^2

- Assuming constant acceleration ( constant applied torque T ) we can determine the angular velocity of the grinding wheel after time t = 10 sec using rotational kinematic equation of motion.

                                      wf = wi + α*t

Where, wf = Final angular velocity (rad/s)

            wi = Initial angular velocity (rad/s)

- Assuming the grinding wheel was initially at rest wi = 0 rad /s. We have:

                                     wf = 0 + 1.25*10

                                     wf = 12.5 rad/s

- The kinetic energy (Ek) of the grinding wheel after 10 seconds can b determined in rotational kinematics terms as follows:

                                     Ek = 0.5*I*wf^2

                                     Ek = 0.5*2.0*12.5^2

                                    Ek = 156.25 J

- The kinetic energy of the grinding wheel after 10 seconds is Ek = 156.25 J

firearm identification is the process of analyzing the bullets and cartridge cases left at a crime scene to determine if they came from a particular firearm. marks on the bullets and cartridges may be common to every firearm of that type. these are called class characteristics.

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 =