# Rotational motion about a fixed axis

• cavery4
In summary, the conversation discusses a problem involving a CD inserted into a player and a radial arm saw. The CD has a mass of 17 g and a radius of 6.0 cm, and accelerates to an angular velocity of 20 rad/s in 0.65 s. The net torque acting on the CD is determined using the formula torque = I * alpha, where I is the inertia and alpha is the acceleration. The correct answer is approx. 9.4 x 10^-4 Nm, but the initial calculation was marked wrong. The second problem involves a circular blade on a radial arm saw, which starts at an angular velocity of 256 rad/s and decreases to 80 rad/s in 17.
cavery4
A CD has a mass of 17 g and a radius of 6.0 cm. When inserted into a player, the CD starts from rest and accelerates to an angular velocity of 20 rad/s in 0.65 s. Assuming the CD is a uniform solid disk, determine the net torque acting on it.

I thought to use: torque = I * alpha (acceleration)
To find Inertia, I did I = 1/2 MR^2
to find acceleration: alpha = (wf - wi)/time or 20 rad/s / .65 seconds
Also, I converted 17 g to .17 kg and 6.0 cm to .06 meters.

My answer was .942. This was marked wrong by webassign. Obviously, I am missing something here. Wrong formula? Missing an important concept? Possibly wrong calculation?

If you point me to my error, I would appreciate this greatly!
I used the above methods to find the correct answer to this problem:

The circular blade on a radial arm saw is turning at 256 rad/s at the instant the motor is turned off. In 17.0 s the speed of the blade is reduced to 80 rad/s. Assume the blade to be a uniform solid disk of radius 0.160 m and mass 0.400 kg. Find the net torque applied to the blade.

What is different about these two problems? What does the radial arm have to do with it?

It can't be.It should be approx. $9.4\cdot 10^{-4} \mbox{Nm}$.

So check your arithmetics again.And those units,too.

Daniel.

thank you!

## What is rotational motion about a fixed axis?

Rotational motion about a fixed axis is the movement of an object around a fixed point or axis. This type of motion can be seen in objects such as spinning tops, wheels, or planets orbiting around a star.

## What is the difference between rotational motion and translational motion?

The main difference between rotational motion and translational motion is the type of movement. In rotational motion, the object rotates around a fixed point or axis, while in translational motion, the object moves in a straight line from one point to another.

## What is angular velocity?

Angular velocity is a measure of how fast an object is rotating around an axis. It is represented by the Greek letter omega (ω) and is measured in radians per second (rad/s) or degrees per second (deg/s).

## What is the relationship between angular velocity and linear velocity?

Angular velocity and linear velocity are related through the formula v = ωr, where v is the linear velocity, ω is the angular velocity, and r is the distance from the axis of rotation to the object. This means that as the angular velocity increases, the linear velocity also increases, and vice versa.

## What is the moment of inertia?

The moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass and distribution of the object's mass around its axis of rotation. Objects with a larger moment of inertia are harder to rotate compared to objects with a smaller moment of inertia.

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