How Do You Calculate Velocity and Acceleration in a Belt and Pulley System?

In summary, in a speed reduction system with three belts and two pulleys, point A on the input belt moves at a constant speed of 0.6m/s to the right. Using the equation Va = Vo + wr, where Vo is the velocity of the center of the left pulley (0m/s), we can determine the angular velocity of the pulley to be 6rad/s clockwise. This means that the pulley is rotating at a speed of 6 x radius of the bigger part of the pulley (0.6m/s). However, it is not clear how to find the velocity and acceleration at points C and B on the output belt and pulley.
  • #1
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Homework Statement



Three belts move over two pulleys without slipping in the speed reduction system. Point A on the input belt moves to the right with a constant spped of 0.6m/s. Determin the velocity of point C on the output belt, and the acceleration of point B on the output pulley.

Homework Equations



Va = Vo + wr
where Vo is the velocity of center of left pulley which is equals to 0m/s
so Va = wr

The Attempt at a Solution



with the above equation I found out that the angular velocity of the pulley is
0.6m/s = (0.1)w
w = 6rad/s clockwise direction
and this means that the pulley is rotating with the speed of 6 x radious of bigger part of pulley = 0.6m/s and from the picture we can deduce that the pulley on the left also rotating with same speed.
This is my assumption and i don't think this is right, and even though this is right how can i find the Vc and acceleration at point B?
 

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  • #2
is Vc = 0.3m/s
and acceleration at point B = 0?
 

FAQ: How Do You Calculate Velocity and Acceleration in a Belt and Pulley System?

What is the definition of "kinematics of rigid body"?

Kinematics of rigid body is the study of the motion of objects that are considered to be rigid, meaning they do not deform or change shape when subjected to external forces.

How is kinematics of rigid body different from kinematics of a particle?

Kinematics of a particle only considers the motion of a single point in space, while kinematics of rigid body takes into account the motion of an entire object and its orientation in space.

What is the difference between translational and rotational motion in kinematics of rigid body?

Translational motion refers to the movement of the center of mass of a rigid body, while rotational motion refers to the rotation of the body about its center of mass.

How is the motion of a rigid body described in kinematics?

The motion of a rigid body is described using quantities such as displacement, velocity, and acceleration, which are vectors that describe the position, rate of change of position, and rate of change of velocity, respectively.

What are some real-world applications of kinematics of rigid body?

Kinematics of rigid body has many practical applications, including analyzing the motion of vehicles, understanding the dynamics of sports movements, and designing machinery and robots for industrial use.

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