# Power Output Given Certain Torque

Jmeeks29ig
Hi,
I have a problem that I've been trying to figure out for a while but cannot seem to get on my own. I'm trying to figure out how much power will be generated in a motor given a certain amount of torque. The problem is, to find the amount of power output , I also need to know the rotational velocity, which I cannot seem to find. I don't know how much resistance the motor would give.

Here's a simple example:
A man rotates a shaft of radius 5 m, with a constant force of 10 N, on a dc motor. How much power does the motor output?

I know that the rotational velocity is missing, as well as the number of turns in the motor, but I don't know how much it would be without knowing the specifications of the motor. If you could steer me in the right direction and maybe give me similar examples, it would be much appreciated, thanks!

Also, how would I know how much resistance the motor provides, in Newtons?

As Power = Torque × Rotational speed, you need to know more.

Lsos
As you seem to understand, without the rpm you simply cannot know. However, assuming that as the man applies 10 N (which would be 50 Nm of torque) the shaft does not accelerate then that means that the resistance is also 10 N (50 Nm). If it wasn't, then the shaft would accelerate until the forces balance out, until the man can't keep up, or until something gets destroyed.

Mentor
Your best bet with the information given is to estimate how fast a person can get around a 5m radius circle.

• Nidum
Gold Member
The rotational speed is going to be impossibly slow for a directly driven dynamo but let's work it out anyway for curiosity :

4 minute mile : 15 mph or 6.7 M/sec
Walking speed : 3 to 5 mph or 1.35 to 2.25 M/Sec

Choose a spot value - say 2 M/sec

Circumference of circle = 10 Pi = 31.42 M .

Revs/sec = 2 / 31.42 = 0.064 rev/sec or 3.8 rpm .

Last edited:
• russ_watters
Homework Helper
Gold Member
You boys have beaten me to it - fortunately, as I'm much more long-winded!
Anyhow, when I got to working out rotational speed, I thought maybe that's not important. 10N at 2m/s is 20W mechanical input power to the dynamo and use whatever gears you need to make that a sensible rotation speed.

The suggestion I would make to OP is, stop thinking of it as a motor and just Google dynamo or DC generator and find endless pages of explanation at all levels

But I hate these cryptic questions: they intrigue me, but frustrate me. I just hope he tells us what it is he really wants to know.

• russ_watters
Jmeeks29ig
Sorry it took so long to get back, but thanks so much for the explanations! That helps me to understand it better. As for the cryptic question, I'm sorry, but I don't know if I'll be able to get much more specific. I want to be able to understand how much power output I will get if I can be applying a constant force to a motor, but it makes it hard when I don't know how fast that shaft will rotate due to the force I place on it. However, it does seem a little bit clearer now!

Homework Helper
Gold Member