How Does Torque Relate to Different Types of Acceleration?

AI Thread Summary
Torque is related to acceleration through the equation τ = Iα, where τ is torque, I is moment of inertia, and α is angular acceleration. For a disk, the moment of inertia is I_z = 1/2 MR^2, leading to the relationship a = 2τ/(MR^3) when substituting α with Ra. The discussion raises a question about the interpretation of linear acceleration a, specifically whether it refers to the linear acceleration of a mass m at the disk's edge. Clarification is sought on the origin of torque, highlighting that it may arise from forces acting close to the axle rather than a single force at a distance R. Understanding these relationships is crucial for solving problems involving rotational dynamics.
saltine
Messages
84
Reaction score
0

Homework Statement


3044245373_1001682a5c.jpg

Find acceleration a given the torque, T, about the axle.

Homework Equations


\tau = I\frac{d\omega}{dt} = I\alpha

Moment of Inertia of a disk (about the axle):
I_z = \frac{1}{2}MR^2

The Attempt at a Solution



\alpha = Ra in this context, so
\tau = I Ra
a = \frac{\tau}{IR} = \frac{2\tau}{MR^3}
I think this is correct, however:

\tau = R \times F, since F = ma, a = \frac{\tau}{mR}.
What does this a represent? Does it represent the linear acceleration of a particle of mass m that happens to be on the edge of the disk?

- Thanks
 
Physics news on Phys.org
Welcome to PF!

Hi saltine! Welcome to PF! :smile:

(i assume the wheel rolls without slipping?)
saltine said:
\alpha = Ra

No, R\alpha = a … just consider the dimensions! :redface:
\tau = R \times F, since F = ma …

No, I don't understand that :confused: … tau doesn't come from a force at a distance R … it probably comes from two forces very close together, on either side of the axle. :wink:
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Analyzing torque of an automobile engine
Replies
6
Views
923
Rod with Current on Rails in Magnetic Field
Replies
12
Views
2K
What's the angular acceleration?
Replies
33
Views
3K
Find moment arm of resultant force of two forces applied at two points
Replies
3
Views
1K
Maxwell disc linked to bar unwinds but stays at same height by raising bar
Replies
2
Views
664
Net Torque Within a Mass and Pulley System
Replies
22
Views
2K
Are the 2nd and 3rd problems in this video correctly solved? (charged dipole and organ pipe problems)
Replies
3
Views
1K
Stretched spring attached to the center of a pure rolling disk
Replies
11
Views
1K
Torque about an accelerating point
Replies
5
Views
3K
Special relativity and acceleration
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top