# Pendulum and roating disc (circular motion)

• bmchenry
In summary, the angle of a rotating pendulum can be used to indicate the speed of rotation of a horizontal disk. When solving for the velocity of the disk, the equation v = sqrt(g (R + l sinθ) tanθ) should be used, with R representing the radius of the disk and l representing the length of the rod holding the pendulum. Using this equation with the given values, the velocity of the disk is calculated to be 0.75 m/s. The incorrect result of 1.88 m/s was due to using the equation for the velocity of the pendulum bob instead of the disk.
bmchenry
A pendulum hanging from the edge of a horizontal disk rotating around an axis at a constant rate. The angle that the rotating pendulum makes with the vertical increases with the speed of rotation and can be used as an indicator of speed, calculate speed of disck if R = 0.2m, l = 0.3m and the angle is 42 degrees
R is radius of disc, l is length of rod holding pendulum

When I solved for the velocity of the disk using v2 = g r tanθ where r =R +lsin(theta)

the nswer was incorrect and it asked me if I solved for the velocity of the bob and not the disk, Which I guess I did beciase I got 1.88m/s. The answer in the book for the problem with the same numbers except theta is 45 was 0.89m/s.
I assume if the angle is smaller in my problem the speed would be less than 0.89, is this correct?
Can anyone explain what I did wrong?

Sorry I do not know how to get the diagram into the question

. Yes, you are correct. Since the angle is smaller in your problem, the speed of the disk should be less than 0.89 m/s. The equation you used to solve for the velocity of the disk is incorrect. You need to use the equation v = sqrt(gr tanθ) where r is the distance from the axis of rotation to the pendulum bob. In this case, the distance from the axis of rotation to the pendulum bob is (R + l sinθ). Therefore, you should use the equation v = sqrt(g (R + l sinθ) tanθ). Plugging in the given values, you should get a velocity of 0.75 m/s.

It is important to clarify what you are trying to calculate in this problem. The formula v2 = grtanθ is used to calculate the velocity of the pendulum bob, not the disk. This formula assumes that the pendulum is swinging at a constant angle θ with respect to the vertical, and the velocity is calculated based on the acceleration due to gravity (g) and the radius of the pendulum (r).

To calculate the speed of the disk, you would need to use a different formula, such as v = ωr, where ω is the angular velocity of the disk and r is the radius of the disk. However, it is not clear from the given information what the angular velocity of the disk is, as it is not specified in the problem. Without this information, it is not possible to accurately calculate the speed of the disk.

Additionally, the angle θ in your problem is given as 42 degrees, while the angle in the book's problem is given as 45 degrees. This difference in angle could also affect the calculated speed of the disk.

In summary, it is important to use the correct formula and have all necessary information in order to accurately calculate the speed of the disk in this problem. Without this information, it is difficult to determine what may have been done incorrectly in your calculation.

## 1. What is a pendulum?

A pendulum is a weight suspended from a pivot point that can freely swing back and forth. It is commonly used in clocks and other timekeeping devices.

## 2. How does a pendulum work?

A pendulum works by utilizing the force of gravity to create a back and forth motion. When the weight is pulled to one side and released, it swings back and forth due to the force of gravity pulling it towards the center point.

## 3. What is circular motion?

Circular motion is a type of motion in which an object moves along a circular path, with a constant speed. This type of motion is characterized by a centripetal force that keeps the object moving in a circular path.

## 4. How is a rotating disc related to circular motion?

A rotating disc is an example of circular motion, as it moves along a circular path. The centripetal force in this case is provided by the friction between the disc and the surface it is rotating on.

## 5. What is the relationship between a pendulum and a rotating disc?

A pendulum and a rotating disc both exhibit circular motion. However, the forces acting on the two objects are different. The pendulum relies on gravity, while the rotating disc relies on friction.

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