# Angular Velocity: Pulley and belt system

• thatstheguy9
In summary: Perhaps you are confusing tangential and angular velocitires.I see where I went wrong. Thanks for your help @haruspex and @Lnewqban.
thatstheguy9
Homework Statement
Determine the angular velocity of Pulley B and C
Relevant Equations
## V = \omega r ##

So far I have:

The velocity of the belt will be the same for pully A and D, so we can calculate the angular velocity of pulley D:

## V_A = V_B ##
## \omega_A r_A = \omega_D r_D ##
## ((20*3)+40)(0.075) = \omega_D (0.025) ##
## \omega_D = 300 Rad/s ##

My next step was to determine the angular velocity of pulley B. My thought was because pully B and pulley D are joined on the same shaft they must have the same velocity.
I determined ## \omega_B = 75 Rad/s ##.
However the solution found ## \omega_B = 300 Rad/s ##.
I don't understand how the larger pulley can have a higher velocity than the smaller pulley. Or why the velocity of pulley A is the same as pulley B. Can someone explain this?

Last edited:
thatstheguy9 said:
Homework Statement:: Determine the angular velocity of Pulley B and C
Relevant Equations:: ## V = \omega r ##

View attachment 290561

So far I have:

The velocity of the belt will be the same for pully A and D, so we can calculate the angular velocity of pulley D:

## V_A = V_B ##
## \omega_A r_A = \omega_D r_D ##
## ((20*3)+40)(0.075) = \omega_D (0.025) ##
## \omega_D = 300 Rad/s ##

My next step was to determine the angular velocity of pulley B. My thought was because they are joined on the same shaft they must have the same velocity.
I determined ## \omega_D = 75 Rad/s ##.
However the solution found ## \omega_D = 300 Rad/s ##.
I don't understand how the larger pulley can have a higher velocity than the smaller pulley. Or why the velocity of pulley A is the same as pulley B. Can someone explain this?
View attachment 290562
You seem to have got yourself confused.
You found ## \omega_D = 300 Rad/s ##, but then changed it to ## \omega_D = 75 Rad/s ##

haruspex said:
You seem to have got yourself confused.
You found ## \omega_D = 300 Rad/s ##, but then changed it to ## \omega_D = 75 Rad/s ##
Apologies, I've corrected the original post.

thatstheguy9 said:
because they are joined on the same shaft
Which two are?

haruspex said:
Which two are?
Pulley B and D

thatstheguy9 said:
Pulley B and D
Ok, so if D's angular velocity is 300r/s what is B's?

haruspex said:
Ok, so if D's angular velocity is 300r/s what is B's?

## V_D = V_B ##
## \omega_D r_D = \omega_B r_B ##
## 300*0.025 = \omega_B * 0.100 ##

thatstheguy9 said:
## V_D = V_B##
Ok, I see. You posted
thatstheguy9 said:
My next step was to determine the angular velocity of pulley B. My thought was because pully B and pulley D are joined on the same shaft they must have the same velocity.
So I thought you meant they must have the same angular velocity. Which is true.

haruspex said:
Ok, I see. You posted

So I thought you meant they must have the same angular velocity. Which is true.
How can they have the same angular velocity when they have different radi?
Which brings me to my next point of confusion:
Why they have used the radius of pulley D to calculate the angular velocity of pulley B.

thatstheguy9 said:
How can they have the same angular velocity when they have different radi?
They're attached rigidly to the same axle. If the axle completes one turn, how many turns, or what fraction of a turn, has each pulley turned?

thatstheguy9 said:
How can they have the same angular velocity when they have different radi?
...
Perhaps you are confusing tangential and angular velocitires.

Lnewqban

## 1. What is angular velocity?

Angular velocity is a measure of the rate at which an object rotates or revolves around a fixed axis. It is typically measured in radians per second or degrees per second.

## 2. How is angular velocity related to pulley and belt systems?

In a pulley and belt system, angular velocity is used to determine the speed at which the pulley rotates, and in turn, the speed at which the belt moves. This is important for calculating the mechanical advantage and efficiency of the system.

## 3. How do you calculate angular velocity in a pulley and belt system?

Angular velocity can be calculated by dividing the linear velocity of the belt by the radius of the pulley. This can also be expressed as the product of the angular speed (in radians per second) and the radius of the pulley.

## 4. What factors can affect the angular velocity in a pulley and belt system?

The angular velocity in a pulley and belt system can be affected by the size and shape of the pulley, the tension in the belt, and any external forces acting on the system, such as friction or gravity.

## 5. How can angular velocity be used to optimize a pulley and belt system?

By understanding the relationship between angular velocity, linear velocity, and mechanical advantage, engineers can use angular velocity to design and optimize pulley and belt systems for specific purposes, such as increasing speed or reducing the force required to lift heavy objects.

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