# Finding angle of change in momentum vector

• Patdon10
In summary, a billiard ball with a mass of 0.250 kg hits a billiard table at an angle of 55.8° and a speed of 27.2 m/s. It bounces off at an angle of 71.0° and a speed of 10.0 m/s. The magnitude of the change in momentum is 5.667 kg*m/s. The change in momentum vector points counter-clockwise from the +x-axis, with a change in the x component of 13.81 m/s and a change in the y component of -15.312 m/s. However, using the equation tan^-1(y component/x component) results in an incorrect angle of -48 degrees.
Patdon10

## Homework Statement

A billiard ball of mass m = 0.250 kg hits the cushion of a billiard table at an angle of θ1 = 55.8° at a speed of v1 = 27.2 m/s. It bounces off at an angle of θ2 = 71.0° and a speed of v2 = 10.0 m/s.

(a) What is the magnitude of the change in momentum of the billiard ball?
(I figured this out to be 5.667 kg*m/s)

(b) In which direction does the change of momentum vector point? (Let up be the +y positive direction and to the right be the +x positive direction.)
(this is where I am absolutely stuck)

## Homework Equations

tan^-1 (y component/x component)

## The Attempt at a Solution

I calculated the velocities into x and y components and then found the change.
The change in the x component of the velocity is 13.81 m/s
The change in the y component of the velocity is -15.312 m/s
multiplying both by the mass of 0.25 kg, we get x = 3.4525, y = -3.828

so tan^-1(-3.828/3.4525) = -48 degrees, but that's not right. Can anyone tell me what I'm doing wrong?

anyone? : /

## 1. What is the definition of "angle of change in momentum vector"?

The angle of change in momentum vector is the measure of the direction and magnitude of the change in an object's momentum over time. It is represented by the angle between the initial momentum vector and the final momentum vector.

## 2. How is the angle of change in momentum vector calculated?

The angle of change in momentum vector can be calculated using the dot product formula: θ = cos-1((P1 • P2) / (|P1| • |P2|)) where P1 and P2 are the initial and final momentum vectors, and θ is the angle of change in momentum vector.

## 3. What factors can affect the angle of change in momentum vector?

The angle of change in momentum vector can be affected by the mass, velocity, and direction of the object, as well as external forces such as friction or collisions with other objects.

## 4. Why is it important to calculate the angle of change in momentum vector?

By calculating the angle of change in momentum vector, we can determine the direction and magnitude of the force acting on an object, and understand how its momentum is changing over time. This information is important for analyzing the motion of objects and predicting their future movements.

## 5. Can the angle of change in momentum vector ever be negative?

No, the angle of change in momentum vector is always a positive value. It represents the amount of change in momentum, which can never be negative. However, the vector itself can change direction, resulting in a negative change in momentum if it is moving in the opposite direction to its initial momentum.

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