Conceptual question about angular speed and radius for rotational motion

[FisherDude]

let's say a wheel rotates with a constant angular acceleration. Would its angular speed be affected if the radius was changed? It seems that angular speed would be independent of the radius since the angle is just a proportional quantity.

 

[dst]

It depends on your assumptions. For a constant angular momentum, the angular frequency decreases with a larger radius - the moment of... something I can't remember at 5:00AM... gets larger since it's proportional to distance from axis - just like a lever.

On the other hand, for a constant angular acceleration, angular acceleration remains... constant.

Edit: Torque. It has the same units as a moment of whatever I can't remember.

 

[FisherDude]

so angular speed is dependent on radius since the force that moves the wheel would cause a greater acceleration if the wheel had a smaller radius (meaning it would be a smaller wheel)? also assuming the force that moves the wheel stays constant.

 

[dst]

Exactly so. Try it yourself, spin around first like a ballerina with your arms extended then like a spinning... cylinder and observe. You will look like a muppet on both accounts but it's all in the name of physics.

 

[FisherDude]

Thanks.

Btw, i will only look like a muppet if someone is looking.

 

[rbj]

Torque, measured in units of force times length has the same dimension as work or energy. and that is legitimate; turning a shaft exactly one radian of twist (and the radian is the mathematically natural unit of twist) the number of Newton-meters of torque becomes exactly the number of Joules of work done. so with a twist of one radian, torque is the same as energy.