Homework Help: Determining Torque

1. Aug 11, 2004

Schu

I am attempting to the following question:
How large is the torque that act on an armature?

Particulars: (can be approximated as a solid cylinder)
length of .124 m
mass of 13.13 kg
Accelerated from REST to operating speed of 3530 rpm in 5.57 second

I know T = F*r
I'm not sure where to start.

Last edited: Aug 11, 2004
2. Aug 11, 2004

pt176900

You are given the mass, the radius, and a change in velocity over a given time interval.

Think of the problem another way:
T = F x r
from Newton's 2nd law: F = m*a
a = dv/dt
so you have: T = m dv/dt x r
start by converting the given velocity into meters per second, then calculating the acceleration. from there it is plug and chug

3. Aug 11, 2004

Staff: Mentor

Newton's 2nd law - for rotational motion

You'll need to apply Newton's 2nd law for rotational motion:
$$\tau = I \alpha$$

You are given all the information needed to calculate I (the rotational inertia) and $\alpha$ (the rotational acceleration).

4. Aug 11, 2004

Corneo

Just to make sure you know that $\tau = r \times F$ not $\tau = F \times r$, it makes a difference. And $||\tau||= rF\sin \phi$

5. Aug 12, 2004

Schu

Now ya'll have me confused again, I thought I was all set with the first formula,
T = f * r. Now where does Newtons Second Law fit into it to get the rotational movement.

Take me step by step if you would.
Thanks for the help so far

6. Aug 12, 2004

Staff: Mentor

Good point, Corneo. (But it won't matter for this particular problem.)

7. Aug 12, 2004

Staff: Mentor

T = r X F is true, but not helpful in this problem. Are you given the force? No.

This is just the rotational analog to an "F = ma" problem. Instead of m, you calculate I; instead of a, you calculate α. Then apply T = I α.

Give it a shot.

8. Aug 12, 2004

Schu

Ok check to see if I am OK on this;
we know T = I α
I = 1/2 mr^2 and α = a / r
so plug it in
I = (1/2) 13.13 * .081^2 = .043072965
α = (29.9425 / 5.57)/.081 = 66.36633641
Multiply the two together for T and you get 2.8585 Nm

How'd I do??

9. Aug 12, 2004

Staff: Mentor

Looks good. Note that you can calculate $\omega$ directly from the rpm, then use it to calculate $\alpha = \omega/t$. Just convert rpm to radians/sec.