# Calculating Applied Torque for a Grinding Wheel

• PeachBanana
In summary, the moment of inertia of a uniform cylinder with a radius of 10.0 cm and a mass of 0.570 kg is 2.85 x 10^-3 kg * m^2. To accelerate the cylinder from rest to 1700 rpm in 4.80s, a net torque of 0.1145 N * m is needed, which is the sum of the applied torque and the frictional torque.
PeachBanana

## Homework Statement

A grinding wheel is a uniform cylinder with a radius of 10.0 cm and a mass of 0.570 kg.

Calculate its moment of inertia about its center.
2.85 x 10^-3 kg * m^2

Calculate the applied torque needed to accelerate it from rest to 1700 rpm in 4.80s if it is known to slow down from 1700 rpm to rest in 57.0s .

## Homework Equations

I = 1/2 Mr^2
ω final - ω initial / t = α
τ = Iα

## The Attempt at a Solution

τ = Iα

τ = (2.85 * 10^-3 kg * m^2)(37.0815 rad./s^2) = 0.1056 N*m (Accelerating from rest to 1700 rpm in 4.80 s)

τ = (2.85*10^-3 kg * m^2)(-3.123 rad./s^2) = -0.00890 N*m (Decelerating from 1700 rpm to rest in 57.0s)

I have these two torques and I'm unsure of what to do with them.

The second bit of info about the slowing down tells you what the frictional torque is. The first bit of info about speeding up tells you what NET torque you need to achieve that acceleration. So, given that frictional torque, what must the *applied* torque be in order to produce the net torque that is required?

net τ = the sum of the magnitudes of the two torques I listed. I added them together and got the correct answer of 0.1145 N * m. Thank you!

PeachBanana said:
net τ = the sum of the magnitudes of the two torques I listed. I added them together and got the correct answer of 0.1145 N * m. Thank you!

Actually, it's

τnet = τapp + τfric

The two that you have are net and frictional. It's applied that you're trying to solve for:

τnet - τfric = τapp

However, since the frictional torque is negative, when you subtract it, it's the same as adding its magnitude. That's why adding the two torques gave you the right answer.

So your arithmetic was right, it was just your interpretation that was a bit off.

Oops. Thank you for correcting me.

## What is the formula for calculating applied torque for a grinding wheel?

The formula for calculating applied torque for a grinding wheel is: Torque = Force x Radius.

## What is the unit of measurement for torque?

The unit of measurement for torque is Newton-meters (Nm) in the SI system, and foot-pounds (ft-lb) in the imperial system.

## How do I determine the force acting on the grinding wheel?

The force acting on the grinding wheel can be determined by using a force gauge or by measuring the weight of the object being ground and multiplying it by the acceleration due to gravity (9.8 m/s²).

## What is the radius of a grinding wheel?

The radius of a grinding wheel varies depending on the specific wheel being used. It is typically measured in millimeters (mm) or inches (in).

## Can I use the same formula for all types of grinding wheels?

Yes, the formula for calculating applied torque can be used for all types of grinding wheels as long as the force and radius are measured accurately.

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