Question

A grinding wheel is a uniform cylinder with a radius of 8.30cm and a mass of 0.400kg .

A)

Calculate its moment of inertia about its center.

Express your answer with the appropriate units.

B)

Calculate the applied torque needed to accelerate it from rest to 2000rpm in 6.00s if it is known to slow down from 1750rpm to rest in 56.0s .

Express your answer with the appropriate units.

Answer 1

The moment of inertia is as follows Here, Mis the mass and R is the radius. Solve for L 10.400 kg)(8.30 em) 2102 m (0.400 kg)(8.30 cm). 1.00 en 0.0014 kg.m2 Now, calculate the angular velocity as follows:

ωΞ 1750 rpm 1750 2π rad pm 60 s 1.00 rpm = 183.16 rad/s The time taken to reach zero rpm, then the time taken is 6.00 s. Hence, the torque applied is as follows: Solve for t =(0.0014 kg-m 183.16 rad/s-0.00 rad/s 56.0 s 0.0045 N.m The expression for the accelerating torque is as follows:

Now, the accelerating acceleration is, 1 min 2π rad 20001 Tpm -Oo 6 s 34.906 rad/s2 -(0.0014) (34.906) 0.048869 N m In Net torque is, τ-0.048869 + 0.0045 0.0534 N m