Agrinding wheel is a uniform cylinder with a radius of 7.80 cm and a mass of 0.550 kg.

part a
calculate its moment of inertia about its center. express your answer to three significant figures and include the appropriate units.
part b
calculate the applied torque needed to accelerate it from rest to 1750 rpm in 7.40 s .

take into account a frictional torque that has been measured to slow down the wheel from 1500 rpm to rest in 58.0 s .

a. I = 167.31 x 10 ⁻³ kg*m²

b. T = 4.59 kg * m² / s²

Explanation:

The moment of inertia of a uniform cylinder:

a.

r = 7.8 cm * 1 m / 100 cm = 0.078 m

I = ½ * m * r²  

I = ½ * 0.55 kg * (0.078²m)

I = 167.31 x 10 ⁻³ kg*m²

b.

T = Iα’ + Iα,    

α’ = ω’/t = 1750 rpm * (2π/60) / 7.40s  =  24.76 rad/s²

α = ω/t = 1500 rpm * (2π/60) / 58  = 2.71 rad/s²

T = (167.31 x 10⁻³ kg*m²)* (24.76 + 2.71 ) rad / s²  

T = 4.59 kg * m² / s²

answer: i pick a

explanation:

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.