# Torque and inertia of a wooden rod

• ac7597
In summary, the given equation represents the inertial mass of a rod and the formula assumes that the mass is uniformly distributed. The mass of the rod is 0.22 kg and the inertial of the rod through the nail is 0.073 kg*m^2. The torque magnitude is 26.5N*m and the angular acceleration of the rod is 363 rad/s^2. However, the calculated inertial of the rod through the nail is 0.073 kg*m^2, which is different from the assumed value of 0.073 kg*m^2. This could be due to the fact that the mass is not uniformly distributed along the rod. Further calculations using the formula for inertial of the rod
ac7597
Homework Statement
A wooden rod sits on the ice of a hockey rink. The rod has a length L=1 meters, but it is made of a peculiar sort of wood. The density changes from the left end to the right, in the following way.

If we measure position x from the left end of the rod, the linear mass density is:
λ(x)=0.2 kg/m + 0.061(x/L)^2 kg/m

What is the mass of the rod?

Joe sticks a nail through the left-hand end of the rod, as shown, and down into the ice. The rod can now rotate around the nail.
What is the moment of inertia of the rod around this nail?

Joe kicks the rod at its middle, applying a force F=53 N perpendicular to the rod as shown in the figure.
What is the magnitude of the torque around the nail due to this force?

The rod now starts to rotate around the nail. What is the magnitude of angular acceleration of the rod?
Relevant Equations
∫ λ(x)=0.2 kg/m + 0.061(x/L)^2 kg/m = 0.2(x) + (0.061/3) (x^3) /(1/L^2)
mass of rod = 0.2+ (0.061/3) =0.22 kg

inertia of rod through nail = (1/3) (mass) (L)^2
inertia of rod through nail = (1/3) (0.22kg) (1m)^2 = 0.073 kg*m^2

torque magnitude = (53N) (0.5m) = 26.5N*m

angular acceleration of the rod= (26.5N*m) / (0.073 kg*m^2)=363 rad/s^2

#### Attachments

• Screen Shot 2019-10-25 at 8.38.06 PM.png
11 KB · Views: 212
inertia of rod through the nail is not 0.073 kg*m^2. I don't know why

ac7597 said:
inertia of rod through nail = (1/3) (mass) (L)^2
This formula assumes that the mass is uniformly distributed along the rod.

dI= (0.2+(0.061/L^2)*x^2 ) dx *x^2
∫dI= I = (0.2x^3)/3 + (0.061x^5)/ (5L^2) |x=1, x=0
I=78.8E-3 kg*m^2

angular acceleration = 26.5N*m / (78.8E-3 kg*m^2) = 336 rad/s^2

## 1. What is torque?

Torque is a measure of the force that can cause an object to rotate around a fixed axis. It is calculated by multiplying the applied force by the distance from the axis of rotation to the point where the force is applied.

## 2. How does torque relate to a wooden rod?

When a force is applied to a wooden rod, it creates a torque that causes the rod to rotate around a fixed axis. The magnitude of the torque depends on the force applied and the distance from the axis of rotation to the point where the force is applied.

## 3. What factors affect the torque of a wooden rod?

The main factors that affect the torque of a wooden rod are the magnitude of the force applied, the distance from the axis of rotation to the point where the force is applied, and the angle at which the force is applied.

## 4. What is inertia and how does it relate to a wooden rod?

Inertia is the property of an object that resists changes in its state of motion. In the case of a wooden rod, its inertia depends on its mass and distribution of mass. This inertia affects how the rod responds to external forces, such as torque.

## 5. How can the torque and inertia of a wooden rod be measured?

The torque of a wooden rod can be measured using a torque sensor or by using a force meter and measuring the distance from the axis of rotation. The inertia of a wooden rod can be measured by calculating its mass and distribution of mass, or by using a moment of inertia sensor.

Replies
2
Views
964
Replies
10
Views
1K
Replies
8
Views
4K
Replies
21
Views
492
Replies
9
Views
1K
Replies
12
Views
1K
Replies
11
Views
3K
Replies
4
Views
1K
Replies
8
Views
2K
Replies
3
Views
2K