A grinding 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.

Question

Physics

Jax Herrera

7 December, 21:28

A grinding 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.

+5

Answers (1)

Know the Answer?

Jayda Donaldson · Answer 1

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