# Homework Problem Involving Forces, Torque, and Moment of Inertia

• tommyhakinen
In summary, the conversation was about a problem involving an applied force and a friction force on a rotating wheel. The total torque produced was 36.0 N·m and the applied force acted for 6.00 s, causing the wheel to increase its angular speed from 0 to 10.0 rad/s. After the applied force was removed, the wheel came to rest in 60.0 s. The homework equations used were \omega_{f} = \omega_{i} + \alpha t, \theta_{f} = \theta_{i} + \omega t + 0.5 \alpha t^{2}, and \tau = I \alpha. The attempt at a solution involved finding the moment of
tommyhakinen

## Homework Statement

The combination of an applied force and a friction force produces a constant total torque of 36.0 N·m on a wheel rotating about a fixed axis. The applied force acts for 6.00 s. During this time the angular speed of the wheel increases from 0 to 10.0 rad/s. The applied force is then removed, and the wheel comes to rest in 60.0 s. Find (a) the moment of inertia of the wheel, (b) the magnitude of the frictional torque, and (c) the total number of revolutions of the wheel.

## Homework Equations

$$\omega_{f} = \omega_{i} + \alpha t$$
$$\theta_{f} = \theta_{i} + \omega t + 0.5 \alpha t^{2}$$
$$\tau = I \alpha$$

## The Attempt at a Solution

I am able to get part (a). However, for part (b) and (c), in order to get the frictional torque and total number of revolutions, I need to get the second angular acceleration from
$$\omega_{f} = \omega_{i} + \alpha t$$
$$0 = 10 + \alpha (10)$$
$$\alpha = -1/6 rad/s^{2}$$

The answer I get is negative. However if I substitute it into
$$\theta_{f} = \theta_{i} + \omega t + 0.5 \alpha t^{2}$$

it becomes
$$\theta_{f} = 10 + 0.5 (-1/6) (60)^{2}$$
$$\theta_{f} = -290 rad$$

it doesn't make sense for it to be negative. advice please. thanks.

Regards,

tommy

well, you've mistakenly put the values as,
tommy said:
$$0 = 10 + \alpha (10)$$

whereas it should be,
$$10 = 0 + \alpha (6)$$,
because, according to the given question, $$\omega_ f$$ is 10 whereas $$\omega_ i$$ is 0. This is evident from the line,

tommy said:
During this time the angular speed of the wheel increases from 0 to 10.0 rad/s.

Now, try working on it!

## 1. What is the difference between force and torque?

Force is a push or pull on an object, while torque is a twisting force that causes rotation. Force is measured in Newtons (N) and torque is measured in Newton-meters (Nm).

## 2. How do you calculate the moment of inertia?

The moment of inertia is calculated by multiplying the mass of an object by the square of its distance from the axis of rotation. It is represented by the symbol "I" and is measured in kg·m².

## 3. What is the relationship between force, torque, and moment of inertia?

Force and torque are both related to moment of inertia, which is a measure of an object's resistance to changes in rotational motion. The greater the moment of inertia, the more force and torque are required to change an object's rotation.

## 4. How does the distribution of mass affect moment of inertia?

The distribution of mass affects moment of inertia because it determines how mass is distributed around the axis of rotation. Objects with a larger mass farther from the axis of rotation have a larger moment of inertia, while objects with a smaller mass closer to the axis have a smaller moment of inertia.

## 5. Can you give an example of a homework problem involving forces, torque, and moment of inertia?

Sure, a common homework problem involving these concepts is calculating the torque required to rotate a door of a given mass and length around its hinges. This would involve finding the moment of inertia of the door, as well as the distance from the axis of rotation to the point where the force is applied.

• Introductory Physics Homework Help
Replies
26
Views
349
• Mechanics
Replies
5
Views
2K
Replies
6
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Mechanical Engineering
Replies
12
Views
635
• Mechanics
Replies
5
Views
729
• Classical Physics
Replies
34
Views
895
• Calculus and Beyond Homework Help
Replies
17
Views
1K
• Introductory Physics Homework Help
Replies
7
Views
567
• Introductory Physics Homework Help
Replies
10
Views
1K