# Angular speed of 2 pulleys on a belt

• MHB
• karush
In summary, the larger pulley rotates 25 times in 36 seconds and has a circumference of 30pi. Its angular speed is 750 cmπ/36 s or 65.5 cm rad/s. The smaller pulley's angular speed can be found using the formula ω2 = (r1/r2)ω1. Substituting values, we get an angular speed of 125π/48 rad/s.
karush
Gold Member
MHB
two pulleys connected by a belt have 15cm and 8cm radius

The larger pulley rotates $25$ times in $36$ sec,

Find the angular speed of each pulleey in radians per second.

the 15cm pulley has circumferce of $30\pi$ so

$\displaystyle\frac{25\text { rev}}{36 \text {sec}} \cdot\frac{30\pi\text{ cm}}{ rev} =\frac{750\text{ cm\pi}}{36\text {sec}} =\frac{65.5\text{ cm}\text{ rad}}{\text{sec}}$

not sure how to get the v of the $$\displaystyle 8cm$$ pulley

Last edited:
Re: angular speed of 2 pulleys on a belt

This is how I would work the first part:

$$\displaystyle \frac{25\text{ rev}}{36\text{ s}}\cdot\frac{2\pi\text{ rad}}{1\text{ rev}}=\frac{25}{18}\pi\frac{\text{rad}}{\text{s}}$$

Angular speed should have units of radians/time.

Since the pulleys are connected by a belt, then the linear velocity of the outer edge of each pulley will be the same:

$$\displaystyle v_2=v_1$$

Using, $$\displaystyle v=r\omega$$, we may state:

$$\displaystyle r_2\omega_2=r_1\omega_1$$

Solve for $$\displaystyle \omega_2$$:

$$\displaystyle \omega_2=\frac{r_1}{r_2}\omega_1$$

Now let $$\displaystyle r_1=15\text{ cm},\,r_2=8\text{ cm},\,\omega_1=\frac{25}{18}\pi\frac{ \text{rad}}{\text{s}}$$

What do you find?

Re: angular speed of 2 pulleys on a belt

$\displaystyle\frac{15}{8}\cdot\frac{25}{18}\pi \text{ = } \frac{125}{48}\pi\ \frac{\text{rad}}{s}$

## 1. What is the formula for calculating the angular speed of 2 pulleys on a belt?

The formula for calculating the angular speed of 2 pulleys on a belt is ω = v/r, where ω is the angular speed in radians per second, v is the linear speed of the belt in meters per second, and r is the radius of the pulley in meters.

## 2. How does the angular speed of a pulley affect the speed of the belt?

The angular speed of a pulley directly affects the speed of the belt. As the angular speed increases, the linear speed of the belt also increases. This is because the pulley is the source of rotation for the belt, and a faster rotation results in a faster movement of the belt.

## 3. Can the angular speed of 2 pulleys on a belt be different?

Yes, the angular speed of 2 pulleys on a belt can be different. This often occurs when one pulley is larger than the other, resulting in a difference in their rotational speeds. However, it is important to note that the linear speed of the belt must remain constant in order to maintain proper tension.

## 4. How is the angular speed of a pulley affected by changes in the belt tension?

The angular speed of a pulley is not directly affected by changes in the belt tension. However, changes in belt tension can cause changes in the linear speed of the belt, which in turn can affect the angular speed of the pulley. This is because the belt tension affects the amount of friction between the belt and the pulley, which impacts the linear speed of the belt.

## 5. How does the radius of a pulley affect its angular speed?

The radius of a pulley directly affects its angular speed. A larger radius results in a slower angular speed, while a smaller radius results in a faster angular speed. This is because the larger the radius, the greater the distance the outer edge of the pulley has to travel to complete one rotation, resulting in a slower rotation speed.

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