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physicsgirl4

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In summary, we are given the initial state of a wheel at rest with an external torque of 60 N m being applied for 12 seconds, resulting in an angular velocity of 800 rev/min. The external torque is then removed and the wheel comes to rest 100 seconds later. Using the equations for torque and angular acceleration, we can determine the moment of inertia of the wheel to be 27kgm^2. However, we must also take into account the frictional torque, which can be solved for by setting up a system of equations using the net torque and angular accelerations for each stage of the wheel's motion.

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physicsgirl4

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Homework Helper

MHB

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physicsgirl4 said:## Homework Statement

1. A wheel is initially at rest. An external torque of 60 N m is applied to the wheel for 12 s, giving the wheel an angular velocity of 800 rev/min. The external torque is then removed, and the wheel comes to rest 100 s later. Find the moment of inertia of the wheel and the frictional torque(constant)

## Homework Equations

torque = moment of interia (I) . angular velocity

angular velocity = dw/dt

## The Attempt at a Solution

angular acceleration = 800.2pi/60.12 = 20/9pi revs/s

That's the right value!

But the wrong unit...

You converted revolutions to radians, and it's an angular acceleration instead of a angular velocity.

The unit should be rad/s

mom of inertia = 60/(20/9) = 27kgm^2

You seem to have lost a pi here...

But the value is not correct yet anyway, since you haven't taken friction into account yet.

Is this correct ? Then I don't know how to find the frictional torque? I have seen the equation net torque = ext torque + frictional torque ..although from this I don't know how to find net torque?

Let's set up the equations first:

In the first stage:

$$T_{net} = T_{ext} - T_{fric} = I \cdot \alpha_1$$

$$T_{ext} = 60 N m$$

$$\alpha_1 = {800 \cdot 2\pi \over 60 \cdot 12} {rad \over s^2}$$

In the second stage:

$$- T_{fric} = I \cdot \alpha_2$$

$$\alpha_2 = - {800 \cdot 2\pi \over 60 \cdot 100} {rad \over s^2}$$

This is a set of equations, can you solve it?

The moment of inertia, also known as rotational inertia, is a measure of an object's resistance to changes in its rotational motion. It is affected by the mass, shape, and distribution of the object.

The moment of inertia can be 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 has units of kg*m^2.

Knowing the moment of inertia of an object is important in understanding its rotational motion. It can help predict how an object will behave when subjected to external forces or torques.

Friction between two surfaces can create a torque, which is a rotational force. This torque can affect the moment of inertia by either increasing or decreasing the object's rotational motion.

Yes, the moment of inertia and frictional torque can be measured through experiments such as the pendulum experiment or the torsion balance experiment. These experiments involve changing the rotational motion of an object and measuring the resulting torque or moment of inertia.

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