How does force and torque affect the acceleration of a rotating object?

[R Power]

we all know that T = F x r
where r is prependicular distance from axis of rotation.
Greater the distance greater will be torque and hence greater angular acceleration for same moment of inertia(i.e same material and axis)

Now, consider a wooden board pivoted at one end. The wooden board is rotated with the help of a motor where it is pivoted. Now we switch on the motor (such that it moves with constant rpm), place a block of considerable weight on the board when it is horizontal, ofcourse the block will fly away like thrown from catapult. Now far the block is placed from pivot, greater the distance it will cover when thrown. This shows that it has greatest acceleration when at max distance from center. This shows max force would have been applied to it by the board when it is at max distance from pivot point. But according to above formula,
for constant torque force varies inversely to distance from center. That means as we go away from fulcrum or the pivot point, less force should be applied to the block (since motor runs at constant rpm) but practically it is not so, far the block is placed far it is thrown.

Can anyone explain?

 

[xxChrisxx]

There are two components to acceleration, a linear motion and rotational. So like a tennis racket or cricket bat hitting a ball, you can get it to go further if you swing the bat in a rotational motion rather than 'pushing' it at the ball.

Not only that but if you add a havy block, and move it out to the edge with a constant torque motor, the RPM will drop due to increases moment of inertia.

 

[russ_watters]

The motor does not move with constant RPM for arbitrarily large torques. There is only so much torque it can give you without burning out.

 

[R Power]

but both angular and linear acceleration at any instant are directly related:

a= alpha x r

alpha=angular acc

 

[R Power]

The motor does not move with constant RPM for arbitrarily large torques. There is only so much torque it can give you without burning out

Imagine something moes it with constant rpm

 

[xxChrisxx]

Imagine something moes it with constant rpm

Then you are making an assumption that is blatantly wrong in reality.

 

[R Power]

Then you are making an assumption that is blatantly wrong in reality.

But there are many points in physics where we take any object moving in a circular motion with constant velocity.

 

[xxChrisxx]

But there are many points in physics where we take any object moving in a circular motion with constant velocity.

Constant andgualr Velocity does not = Constant torque to give a set RPM.

If you took a motor rated at 100rpm at 10kg.m torque. If you then loaded it up to 20kg.m you would obviously not get 100rpm. Of course you could measure what RPM you did get and assume that is constant for that loading.

Also you are appraoching this a very odd way.
You don't need to even consider the force, as the block is already moving at it's maximum speed.

 

[R Power]

so constant torque isn't possible in this world?

 

[xxChrisxx]

so constant force isn't possible in this world?

I have no idea what this has to do with anything relevent.

EDIT: You change ze Q :P

so constant torque isn't possible in this world?

Constant RPM certainly isn't possible with a set torque but varying load.

This is all irrelevant to the OP anyway. You are applying force principles where it isn't needed, and thus getting a non intuative answer. It's a very simple application of conservation of momentum.

 

[R Power]

i'm sorry it was torque not force I've edited that

 

[Redbelly98]

Since this was essentially a thought experiment, a constant-rpm source is no more absurd than a constant current or voltage source in electronics. If you don't like that, then assume constant rpm over some operating range that we'll agree to stay within.

In the OP, assuming constant rpm leads to one conclusion. Then assuming a constant torque leads to a different conclusion. It isn't a problem, since these are two different situations.

 

[Lsos]

Now, consider a wooden board pivoted at one end. The wooden board is rotated with the help of a motor where it is pivoted. Now we switch on the motor (such that it moves with constant rpm), place a block of considerable weight on the board when it is horizontal, ofcourse the block will fly away like thrown from catapult. Now far the block is placed from pivot, greater the distance it will cover when thrown. This shows that it has greatest acceleration when at max distance from center. This shows max force would have been applied to it by the board when it is at max distance from pivot point. But according to above formula,
for constant torque force varies inversely to distance from center. That means as we go away from fulcrum or the pivot point, less force should be applied to the block (since motor runs at constant rpm) but practically it is not so, far the block is placed far it is thrown.

The reason you're confused is, quite simply, because the part that I bolded is wrong. Practically it IS so. You can't just increase the weight of the thrown block, or increase it's distance from the center and expect it to go flying faster.

The situation you described, where the motor has constant rpm and constant torque...simply would not work in the real world. If we increase the weight of the block or its distance to center, something HAS to change, whether it's the rpm (hence the speed at which it's thrown) or the torque.

If not, then it's a clear violation of conservation of energy. So, it's good that doesn't make sense to you. It shouldn't make sense to you, because it DOESN'T work.

I'm not sure why you think it would work. Perhaps you've never actually tested it in real life. If you DO test it, I assure you that everything would make sense mathematically and physically. You do need to make some measurements though...the speed of the projectile or the distance thrown, and vary the torque or rpm applied. Don't just eye it.

Oh, and very important, make sure the projectile actually has a significant weight. If you use a castle-siege type catapult and use a pebble as the projectile then obviously you wouldn't see any difference. It would be kind of like trying to throw a grain of sand, or two grains of sand. They will leave your hand at the same speed, because all of your energy is going into accelerating your hand...not the sand.