• 24forChromium
In summary: You have no way of finding the force of the point mass on the shaft.In summary, the relationship between torque and angular acceleration is analogous to F=ma. You cannot find the force exerted by the point mass on the shaft using the equation Tauapp. - Tauresistance because the net torque is due only to external forces.
24forChromium

## Homework Statement

A lever with one end on a pivot point, a point mass on the lever's shaft with a certain arm length (d), it is also the only relevant mass body (m). A torque (Tauapp.) is applied to the lever, an angular acceleration (alpha) transpired. Find the relationship between the force received by the point mass and the other variables.

## Homework Equations

alpha = Tau / mass (...)
Freceived = -Fpoint on shaft (as the shaft moves, a force is conferred on the point mass, the point mass in return exerts a force on the shaft in the opposite direction)

## The Attempt at a Solution

ΣTau = m*alpha
Tauapp. - Tauresistance = m*alpha
Tauapp. - Fpoint on shaft*d= m*alpha

The units of Tau/mass are not units of angular acceleration.

Nathanael said:
The units of Tau/mass are not units of angular acceleration.
What is it then? (if it is anything) and what should be the unit of angular acceleration?

The unit of angular acceleration is (time)-2

What is the relationship between torque and angular acceleration? It's analogous to F=ma

Nathanael said:
The unit of angular acceleration is (time)-2

What is the relationship between torque and angular acceleration? It's analogous to F=ma
Sorry I was stupid, Tau = MomentOfInertia * angular acceleration

24forChromium said:
Freceived = -Fpoint on shaft (as the shaft moves, a force is conferred on the point mass, the point mass in return exerts a force on the shaft in the opposite direction)
This is not really a useful equation. You have no way of finding the force of the point mass on the shaft.

Try to find the (linear) acceleration of the point mass so you can use F=ma

Nathanael said:
This is not really a useful equation. You have no way of finding the force of the point mass on the shaft.

Try to find the (linear) acceleration of the point mass so you can use F=ma

Why can't I find the force exerted by the point mass on the shaft? What I was thinking is, at a specific moment in time, if there is an angular acceleration, then there must be a net torque, the net torque is made up of components, the applied torque and the resisting torque, the resisting torque, in my opinion, can only be the result of the point mass pushing back against the shaft, thus, by finding the net torque, the applied torque, the arm length to the torque by the point mass, one can find the force of the point mass on the shaft, it is what I am trying to find.

But I guess the angular acceleration of the shaft can be "translated" into the linear acceleration of the point, say it's 90degrees/second^2, and the point mass is 10m away from the axis, since alpha=acceleration/radius, acceleration = alpha*radius = 90°/s2 * 10m= 1.59m/s^2
Once we get the linear acceleration, just use the mass to deduce the received force.

Last edited:
24forChromium said:
Why can't I find the force exerted by the point mass on the shaft? What I was thinking is, at a specific moment in time, if there is an angular acceleration, then there must be a net torque, the net torque is made up of components, the applied torque and the resisting torque, the resisting torque, in my opinion, can only be the result of the point mass pushing back against the shaft, thus, by finding the net torque, the applied torque, the arm length to the torque by the point mass, one can find the force of the point mass on the shaft, it is what I am trying to find.
The point mass pushes on the shaft and the shaft pushes on the point mass. Both of these (equal and opposite) forces produce an equal and opposite torque which cancels out. These are called "internal forces" because both of forces (the "action and reaction" forces) act within the system, so their effect cancels out and can be ignored. The net torque is due only to external forces.

24forChromium said:
acceleration = alpha*radius = 90°/s2 * 10m
It is important that you measure alpha in radians per second per second (not degrees per second^2) before you multiply it by the radius. This formula (alpha*radius=acceleration) is only true when alpha is measured in radians per second^2

The reason is because the length of an arc on a circle is R*θ if θ is measured in radians (that's essentially the definition of radians and it's why it's such a useful and natural unit.)
(θ is the angle subtended by the arc we are measuring and R is the radius of the circle)

Nathanael said:
The point mass pushes on the shaft and the shaft pushes on the point mass. Both of these (equal and opposite) forces produce an equal and opposite torque which cancels out. These are called "internal forces" because both of forces (the "action and reaction" forces) act within the system, so their effect cancels out and can be ignored. The net torque is due only to external forces.It is important that you measure alpha in radians per second per second (not degrees per second^2) before you multiply it by the radius. This formula (alpha*radius=acceleration) is only true when alpha is measured in radians per second^2

The reason is because the length of an arc on a circle is R*θ if θ is measured in radians (that's essentially the definition of radians and it's why it's such a useful and natural unit.)
(θ is the angle subtended by the arc we are measuring and R is the radius of the circle)

Okay, I did that, and I got this:
Force on point mass = 1.59m/s^2

Now, is it correct to say that:
Force on point mass = (Moment of Inertia * angular acceleration - torqueapplied) / arm length of point mass
?

24forChromium said:
Okay, I did that, and I got this:
Force on point mass = 1.59m/s^2
Units should be kg*m/s^2 but that's probably just a typo.
I can't tell you if this is correct because the problem statement in your OP did not have any numbers in it.

24forChromium said:
Now, is it correct to say that:
Force on point mass = (Moment of Inertia * angular acceleration - torqueapplied) / arm length of point mass
?
Moment of inertia * angular acceleration equals the applied torque, so your equation will always be zero.

24forChromium

## 1. How do I determine the direction of rotation?

The direction of rotation can be determined by using the right-hand rule. Point your thumb in the direction of the rotation and your fingers will curl in the direction of the rotation.

## 2. What is the formula for calculating rotational velocity?

The formula for rotational velocity is ω = Δθ/Δt, where ω is the angular velocity, Δθ is the change in angle, and Δt is the change in time.

## 3. How do I find the moment of inertia for a rotating object?

The moment of inertia can be found by multiplying the mass of the object by the square of its distance from the axis of rotation. It is represented by the symbol I and is measured in kg·m^2.

## 4. What is the difference between rotational and linear motion?

Rotational motion refers to the movement of an object around an axis, while linear motion refers to the movement of an object in a straight line. Rotational motion also involves the concept of torque, while linear motion involves the concept of force.

## 5. How does rotational motion affect the stability of an object?

The stability of an object is affected by its moment of inertia, which is determined by its shape and distribution of mass. Objects with a larger moment of inertia are more stable and less prone to tipping over, while objects with a smaller moment of inertia are less stable and more likely to tip over.

Replies
7
Views
761
Replies
97
Views
4K
Replies
7
Views
666
Replies
3
Views
864
Replies
32
Views
1K
Replies
5
Views
2K
Replies
5
Views
2K
Replies
7
Views
1K
Replies
10
Views
1K
Replies
5
Views
3K