# Physics 12u - Two masses Spinning on a disc

• MHB
• Wild ownz al
In summary, if the block is fully on the disk and the center of the block is at a distance $r$ from the axis of rotation, the static friction will be $F_s=\mu_{s}N$ and the centripetal force will be $F_c=m\omega^2r$.
Wild ownz al
A penny of mass 3.10 g rests on a small 20.0-g block supported by a spinning disk. The block is sitting at the edge of the disc at a radius of 12 cm. If the coefficient of friction between block and disk are 0.750 (static) and 0.640 (kinetic) while those for the penny and
block are 0.450 (kinetic) and 0.520 (static), what is the maximum rate of rotation (in revolutions per minute) that the disk can have before either the block or the penny starts to slip?

Last edited:
Wild ownz al said:
A penny of mass 3.10 g rests on a small 20.0-g block supported by a spinning disk. If the coefficient of friction between block and disk are 0.750 (static) and 0.640 (kinetic) while those for the penny and
block are 0.450 (kinetic) and 0.520 (static), what is the maximum rate of rotation (in revolutions per minute) that the disk can have before either the block or the penny starts to slip?

Hi wild one,

That depends on the distance of the block and the cent from the axis of rotation.
Is that given?

Either way, since we're talking about 'starts to slip', we're only interested in the static friction.
Since the block has the lower coefficient of static friction, the block will be the first to slip.
The block will start to slip when the centrifugal force on the block is equal to its static friction.

Klaas van Aarsen said:
Hi wild one,

That depends on the distance of the block and the cent from the axis of rotation.
Is that given?

Either way, since we're talking about 'starts to slip', we're only interested in the static friction.
Since the block has the lower coefficient of static friction, the block will be the first to slip.
The block will start to slip when the centrifugal force on the block is equal to its static friction.

Hey sorry I missed that. I updated the question including the radius.

Wild ownz al said:
Hey sorry I missed that. I updated the question including the radius.

Hmm... we still need the location of the block...
Is it at the edge of the disk? Then we need to know the size of the block. Is it given?
Or can we assume the disk is a little bigger and the center of the block is at the given radius?

Anyway, let's assume that the block is fully on the disk, and that the center of the block is at a distance $r$ from the axis of rotation.

Then the static friction $F_s$ on the block, just before it starts sliding, is
$$F_{s} = \mu_{s} N\tag 1$$
where $\mu_{s}$ is the coefficient of static friction of the block with the disk, and $N$ is the combined weight of the block and the cent.

The corresponding centripetal force $F_c$ is
$$F_c=m \omega^2 r \tag 2$$
where $m$ is the combined mass of the block and the cent, and $\omega$ is the angular velocity.

The combined weight is
$$N= m g\tag 3$$
where $m$ is again the combined mass, and $g=9.81\,\text{m/s}^2$.

The angular velocity is
$$\omega = 2\pi f\tag 4$$
where $f$ is the frequency, which is the number of revolutions per second.

Finally, we have that
$$f = \frac{rpm}{60} \tag 5$$
where $rpm$ is the revolutions per minute.

Set $F_{s}=F_c$ and solve for $rpm$?

Klaas van Aarsen said:
Hmm... we still need the location of the block...
Is it at the edge of the disk? Then we need to know the size of the block. Is it given?
Or can we assume the disk is a little bigger and the center of the block is at the given radius?

Anyway, let's assume that the block is fully on the disk, and that the center of the block is at a distance $r$ from the axis of rotation.

Then the static friction $F_s$ on the block, just before it starts sliding, is
$$F_{s} = \mu_{s} N\tag 1$$
where $\mu_{s}$ is the coefficient of static friction of the block with the disk, and $N$ is the combined weight of the block and the cent.

The corresponding centripetal force $F_c$ is
$$F_c=m \omega^2 r \tag 2$$
where $m$ is the combined mass of the block and the cent, and $\omega$ is the angular velocity.

The combined weight is
$$N= m g\tag 3$$
where $m$ is again the combined mass, and $g=9.81\,\text{m/s}^2$.

The angular velocity is
$$\omega = 2\pi f\tag 4$$
where $f$ is the frequency, which is the number of revolutions per second.

Finally, we have that
$$f = \frac{rpm}{60} \tag 5$$
where $rpm$ is the revolutions per minute.

Set $F_{s}=F_c$ and solve for $rpm$?

Updated the question again with the location of the masses. However there are no sizes of the masses given

Wild ownz al said:
Updated the question again with the location of the masses. However there are no sizes of the masses given

Can it be that we should read it as: "The block is sitting at the edge of the disc at a radius of 12 cm?"

If so, then we can proceed with $r=12\,\text{cm}$.

Klaas van Aarsen said:
Can it be that we should read it as: "The block is sitting at the edge of the disc at a radius of 12 cm?"

If so, then we can proceed with $r=12\,\text{cm}$.

That is correct.

Wild ownz al said:
Updated the question again with the location of the masses. However there are no sizes of the masses given

your original post gives mass measurements for the penny & block ...

A penny of mass 3.10 g rests on a small 20.0-g block supported by a spinning disk.

skeeter said:
your original post gives mass measurements for the penny & block ...

Hey Skeeter. I read his question as if he was looking for the actual dimensions of the objects. The masses of the block and penny are given.

Yeah, I meant the actual sizes.
Either way, it does say that the block is 'small', suggesting that we can ignore its size.

So?
How far do you get if you don't mind me asking?

## 1. What is the purpose of studying two masses spinning on a disc in Physics 12u?

The purpose of studying two masses spinning on a disc in Physics 12u is to understand the principles of rotational motion and how it applies to real-world situations. This experiment allows students to observe and analyze the relationship between the masses, the disc, and the forces acting upon them.

## 2. What equipment is needed to conduct this experiment?

To conduct this experiment, you will need a disc with two masses attached, a support stand, a stopwatch, a ruler, and a string. You may also need a protractor to measure angles and a force probe to measure the forces acting on the masses.

## 3. What are the key concepts that can be learned from this experiment?

This experiment can help students understand concepts such as angular velocity, angular acceleration, centripetal force, and the relationship between force and acceleration in rotational motion. It also allows students to apply these concepts to calculate and analyze the motion of the masses on the disc.

## 4. How can this experiment be modified to investigate different scenarios?

This experiment can be modified by changing the masses, the radius of the disc, or the angle at which the string is attached. This will result in different values for angular velocity, acceleration, and centripetal force, allowing students to observe and analyze the effects of these changes on the motion of the masses.

## 5. What are some real-world applications of this experiment?

Understanding rotational motion and the principles learned from this experiment can be applied to various real-world scenarios, such as the motion of planets and satellites, the rotation of tires on a car, and the spinning of a figure skater. It can also be used in engineering and design to optimize the performance of rotating machinery and structures.

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