Physics: Vector Help - Magnitude & Angle Calculations

In summary, the conversation discusses finding the magnitude and angle of a resultant vector and the components of a vector. It also mentions the relationship between components and magnitude, and clarifies the meaning of counter-clockwise and clockwise angles.
  • #1
buffgilville
91
0
Can someone please help me with this?
1) A resultant vector is 5 units long and makes an angle of 23 degrees measured counter-clockwise with respect to the positive x-axis. What are the magnitude and angle (measured counter-clockwise with respect to the positive x-axis) of the equilibrant vector?

2) Find the x- and y-components of the vector whose magnitude is 8.73 units making an angle of 155 degrees measured counter-clockwise with respect to the positive x-axis.
 
Physics news on Phys.org
  • #2
These kinds of questions have already been answered, look at some other posts.

Think of the fact that the x-component of a vector of magnitude F and angle x with the x-axis is
equal to F*cos (x). The y-component is F*sin(x)

Once the components are given you can work the other way around and determin the magnitude of the vector as F = sqrt(x² + y²)

regards
marlon
 
  • #3
But what does the counter-clockwise mean? Does it mean that the angle is negative? I'm confused.
 
Last edited:
  • #4
Clockwise means a negative angle, and counter-clockwise means a positive angle.
 

1. What is a vector?

A vector is a mathematical quantity that has both magnitude and direction. In physics, vectors are used to represent physical quantities such as force, velocity, and acceleration.

2. How do you calculate the magnitude of a vector?

The magnitude of a vector can be calculated using the Pythagorean theorem, which states that the magnitude (length) of a vector is equal to the square root of the sum of the squares of its components. In other words, to calculate the magnitude of a vector with components x and y, we use the formula: magnitude = √(x^2 + y^2).

3. What is the difference between a scalar and a vector?

A scalar is a mathematical quantity that has only magnitude, while a vector has both magnitude and direction. For example, temperature is a scalar quantity as it only has a numerical value, but velocity is a vector quantity as it has both magnitude and direction.

4. How do you calculate the angle of a vector?

The angle of a vector can be calculated using trigonometric functions. For a vector with components x and y, the angle θ can be found using the formula: θ = tan^-1 (y/x). Alternatively, the angle can also be found using the dot product of two vectors: θ = cos^-1 (a•b / |a||b|), where a and b are the two vectors and |a| and |b| are their magnitudes.

5. Can a vector have a negative magnitude?

No, a vector cannot have a negative magnitude. Magnitude is a scalar quantity and therefore cannot be negative. However, a vector can have a negative direction, which indicates the direction opposite to its positive direction. For example, a velocity vector with a magnitude of 10 m/s and a direction of -30 degrees is equivalent to a velocity vector with a magnitude of 10 m/s and a direction of 330 degrees.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
203
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
3K
  • Introductory Physics Homework Help
Replies
21
Views
2K
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
9
Views
2K
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
13
Views
2K
  • Introductory Physics Homework Help
Replies
13
Views
1K
Back
Top