# Relationship between torque, speed, and mass (Need Help Quickly!)

1. Oct 17, 2009

### infinite_gbps

Hi,

I am having a hard time understanding the relationship between torque, angular speed, & required mass of an object. Angular accerlation notwithstanding.

Can someone help me understand how the ability of a machine to spin faster reduces the requirement for torque to generate a specific power and then subsequently reduces the necessary mass of the rotating object?

I am really concerned of the latter part.

2. Oct 17, 2009

### xxChrisxx

i'm having a bit of trouble understanding this question.

First lets look at what each of the terms means.

Power - Rate at which work is performed.
Work - Energy transferred by a force over a given distance.

Torque - A twisting 'force'. The linear equivilant to this is force.
Angular velocity = equivilant to linear distance / time. (speed)

First i'll deal with the linear equivilant.

Work = Force * Distance travelled
Power = Work / Time

We can rewrite this as

P = F*D/T
P = Force * Velocity.

To keep the same power output if force increases velocity must decrease.

Imagine pushing a large block of concrete along the floor. You need to move it a certain distance. You can either push it hard but not as often. Or with less effort but more often.

Torque is the rotational equivilant of force. Angular velocity is the angular equivilant of velocity.

so P = Tw.

The reduced mass of a rotating object isnt strictly true. It is moment of inertia that counts.

Lets take the linear equivilant again.

Force = Mass * acceleration
P = F*D/T

Reducing the mass reduced the force applied.

Moment of inertia is the rotational equivilant of mass. (sometimes its called angular mass).

I = R^2 M

Torque created by a rotating object is the angular equivilant to newtons second law.

T = Ia

whree I is MOI and a is angular acceleration.

REducing the moment of inertia (by either reducing the radius of the mass or the mass itsself) reduces the torque output of the object.