i have circle with a diamiter of 12m. and a force aplied tangent to this circle of 10N how would i find rpm's

Question

if i had a circle with a radius of six and a force aplied to the tangent of the cirlce of 10N then there would be a Torque 60 NM if this was aplied constatly would the rotational speed of the circle increase? and if so how whould i calculate this. if you cuold email me @ [e-mail] it would be great.

Answer 1

The angular frame of reference has equations of motion that are analogous to the translation al frame.
The angular speed is related to acceleration as

ω(t)=ω0+α*t
And angular displacement is

θ(t)=θ0+ω0*t+0.5*α*t^2

Torque is related to angular acceleration as
T=I*α
where I is the moment of inertia

Also, energy is analogous
KE=.5*I*ω^2
and work is
W=T*θ

In your case, the 60 Nm torque would result in acceleration of

α=60/I
which you can plug into
ω(t)

In order to calculate the numbers you need the mass of the circle and the time or angular displacement.

j

Answer 2

the word 'circle' does not mean anything. You have to state the shape of the rotating object whether it is a thin ring or a circular disk of uniform thickeness. Also mass of the object is required. Once this information is available, angular acceleration can be calculated and then the rpm at a particular instant because rpm keeps increasing as long as the torque is being applied.