# Question on Moment of Inertia/Rotational Inertia

• i_hate_math
In summary, a wheel of radius 0.42 m is connected to a 2.7 kg box via a frictionless cord and inclined surface. The box accelerates down the surface at 1.9 m/s2. To find the rotational inertia of the wheel, the tension in the cord must be calculated. This can be done by considering the free body diagrams of both the wheel and the block, taking into account the forces and accelerations of each object. The tension affects both objects and must be taken into account in the equation for rotational inertia.
i_hate_math

## Homework Statement

In the figure, a wheel of radius 0.42 m is mounted on a frictionless horizontal axle. A massless cord is wrapped around the wheel and attached to a 2.7 kg box that slides on a frictionless surface inclined at angle θ = 28 owith the horizontal. The box accelerates down the surface at 1.9 m/s2. What is the rotational inertia of the wheel about the axle?

Diagram attached

## Homework Equations

Torque=Moment of Inertia*angular acceleration
F=ma

## The Attempt at a Solution

what i did was combinr the equations and yielded the following
I=(F*r^2)/a=0.47628
I don't see where I did wrong but the solution does not match

#### Attachments

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i_hate_math said:
I=(F*r^2)/a
You don't say how you calculate the tension. We cannot tell where you went wrong if you do not post your working.

I just realized what I calculated was Fa instead of tension. But how do i find the tension?? I don't know what to do with the angle ø=28°. pls help
haruspex said:
You don't say how you calculate the tension. We cannot tell where you went wrong if you do not post your working.

i_hate_math said:
I just realized what I calculated was Fa instead of tension. But how do i find the tension?? I don't know what to do with the angle ø=28°. pls help
You should draw free body diagrams for both objects, the wheel and the block. Consider the forces on each, the accelerations of each and the relationships between them. The tension affects both.

i_hate_math
haruspex said:
You should draw free body diagrams for both objects, the wheel and the block. Consider the forces on each, the accelerations of each and the relationships between them. The tension affects both.
thanks heaps, i see what went wrong now. Guess i shouldve drawn a bid and clear free body diagram at the first place!

## 1. What is moment of inertia/rotational inertia?

Moment of inertia, also known as rotational inertia, is a measure of an object's resistance to changes in its rotational motion. It is similar to mass in linear motion, as it describes the object's tendency to resist changes in its rotational velocity.

## 2. How is moment of inertia/rotational inertia calculated?

The moment of inertia of an object is calculated by multiplying the mass of the object by the square of its distance from the axis of rotation. It is also affected by the distribution of mass around the axis of rotation.

## 3. What is the relationship between moment of inertia/rotational inertia and angular acceleration?

The moment of inertia and angular acceleration are inversely proportional. This means that the larger the moment of inertia, the smaller the angular acceleration will be for a given torque. In other words, objects with larger moments of inertia will require more torque to achieve the same angular acceleration as objects with smaller moments of inertia.

## 4. How does the shape of an object affect its moment of inertia/rotational inertia?

The shape of an object plays a significant role in determining its moment of inertia. Objects with a larger radius of rotation or objects that are more spread out around the axis of rotation will have a larger moment of inertia compared to objects with a smaller radius or objects that are more compact.

## 5. What are some real-life applications of moment of inertia/rotational inertia?

Moment of inertia is an important concept in many fields of science and engineering. Some common applications include understanding the stability of structures, designing flywheels for energy storage, and predicting the motion of celestial bodies in space. It is also used in sports equipment design, such as in the design of golf clubs and tennis rackets to optimize their performance.

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