Ball in Vertical Circle on End of String, Tangential and Radial Acceleration

In summary: That means that the center of rotation is to the right and slightly above the ball.In summary, a ball swings in a vertical circle at the end of a rope and at a certain point, its total acceleration is (-22.5 i + 20.2 j) m/s2. The goal is to determine the magnitude of its radial acceleration and the speed and velocity of the ball. To find the radial acceleration, we need to subtract the tangential acceleration from the total acceleration. However, the tangential acceleration is unknown and must be calculated using the given information. The j vector in the acceleration vector points towards the center of rotation, which is slightly above and to the right of the ball.
  • #1
xslc
6
0

Homework Statement



A ball swings in a vertical circle at the end of a rope 1.30 m long. When the ball is 36.1° past the lowest point on its way up, its total acceleration is (-22.5 i + 20.2 j) m/s2.

(a) Determine the magnitude of its radial acceleration.

(b) Determine the speed and velocity of the ball.

Homework Equations



A = v^2/r
Ar = Atotal - Atangential

The Attempt at a Solution



I have no idea where to go with this. I am stuck on the first part. My issue is in figuring out the tangential acceleration so that I can subtract that from the total acceleration to find the radial/centripetal acceleration. My thought is that tangential acceleration should be zero, because the ball is swinging on the end of a string, and its speed should not be changing, only its velocity.
 
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  • #2
You have a=(-22.5 i + 20.2 j) m/s2. The acceleration vector is made up of the sum of the radial and tangential acceleration. Using your coordinate system, the j vector points up or towards the center of rotation right? So the radial acceleration is?
 
  • #3
rock.freak667 said:
You have a=(-22.5 i + 20.2 j) m/s2. the j vector points up or towards the center of rotation right?

no, up is not towards the center of rotation. it is 36.1 degrees past the bottom
 

What is the relationship between tangential and radial acceleration in a ball in vertical circle on end of string?

In a ball in vertical circle on end of string, tangential acceleration and radial acceleration are both present and are dependent on each other. As the ball moves in a circle, it experiences a change in direction and velocity, which causes a tangential acceleration. This tangential acceleration is also responsible for creating a radial acceleration, which keeps the ball moving in a circular path.

How does the radius of the circle affect the tangential and radial acceleration of a ball in vertical circle on end of string?

The radius of the circle has a direct impact on the magnitude of both the tangential and radial acceleration. As the radius increases, the tangential acceleration decreases while the radial acceleration increases. This is because a larger radius means a larger distance to travel in the same amount of time, resulting in a slower tangential acceleration and a higher radial acceleration to maintain the circular motion.

What factors influence the tangential and radial acceleration of a ball in vertical circle on end of string?

The tangential and radial acceleration of a ball in vertical circle on end of string are influenced by several factors, including the mass of the ball, the velocity of the ball, and the radius of the circle. The greater the mass and velocity of the ball, the higher the tangential and radial acceleration will be. The radius of the circle also plays a role, as a larger radius will result in lower tangential acceleration and higher radial acceleration.

How is the centripetal force related to the tangential and radial acceleration in a ball in vertical circle on end of string?

The centripetal force, which is the force that keeps the ball moving in a circular path, is directly proportional to the radial acceleration. This means that as the radial acceleration increases, so does the centripetal force. The tangential acceleration, on the other hand, does not directly affect the centripetal force.

How do tangential and radial acceleration change as the ball in vertical circle on end of string moves through different points in the circle?

As the ball moves through different points in the circle, both the tangential and radial acceleration change. At the top of the circle, the tangential acceleration is zero and the radial acceleration is equal to the gravitational acceleration. As the ball moves down the circle, the tangential acceleration increases while the radial acceleration decreases. At the bottom of the circle, the tangential acceleration is at its maximum and the radial acceleration is zero. Finally, as the ball moves up the circle, the tangential acceleration decreases while the radial acceleration increases.

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