Pulley Problems with Rotation

In summary, the problem involves two wheels, A and C, connected by a belt with radii of 10 cm and 25 cm respectively. Wheel A starts from rest and increases its angular speed at a rate of 1.6 rad/s^2. The goal is to determine the time it takes for wheel C to reach a rotational speed of 100 rev/min, using the equations of motion. There is confusion on how to approach the problem, with one suggestion of solving for A and then multiplying by 2.5. However, there is uncertainty on how to incorporate the variable theta, which relates to the radius.
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1. Wheel A of radius 10 cm is coupled by belt B to a wheel C of radius 25 cm. Wheel A increases its angular speed from rest at a uniform rate of 1.6 rad/s^2. Determine the ime required for wheel C to reach a rotational speed of 100 rev/min, assuming the belt does not slip



2. I'm very confused by what exactly I have to solve for first. I know that I have to use the 5 equations of motion (with the rotation variables subbed in for the linear ones) but I'm still not sure.



3. I thought that since the radius of C is A*2.5, I thought about solving for A, and then multiplying by 2.5, but I don't know... Can someone please show me how to do it?
 
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  • #2
by coupled, it means that the two wheels are connected by a belt that goes around them, like a rubber band.
 
  • #3
wf^2-wi^2=2a(theta) is what I'm thinking of using, but I don't know where to get (theta) in relation to the radius. i know that theta r = d, but there's no "d"

:(
 

1. How do pulleys affect rotational motion?

Pulleys can change the direction and magnitude of rotational motion by redirecting the force applied to the system. This is because they utilize the principle of torque, which is the force applied at a distance from the axis of rotation.

2. What is the difference between a fixed and movable pulley in rotational motion?

A fixed pulley does not rotate and only changes the direction of the force, while a movable pulley rotates and can also change the magnitude of the force applied to the system.

3. How do you calculate the mechanical advantage of a pulley system?

The mechanical advantage of a pulley system is equal to the number of rope segments supporting the weight. For example, a system with 4 rope segments supporting the weight has a mechanical advantage of 4.

4. Can pulleys be used to increase the efficiency of a rotational system?

Yes, pulleys can be used to increase the efficiency of a rotational system by reducing the amount of force needed to move an object. This is due to the fact that pulleys distribute the force over multiple rope segments, reducing the overall force required.

5. What are some real-life applications of pulleys in rotational systems?

Pulleys are commonly used in machines and equipment, such as cranes and elevators, to lift heavy objects. They are also used in bicycles to transfer power from the pedals to the wheels through a rotating system. Additionally, pulleys can be found in engines and other mechanical systems to change the direction of rotational motion.

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