Someone please check my simple vector algebra

In summary, the conversation involved finding the velocity, position, angular momentum, acceleration, and torque vectors for a .5kg body at t=1s to t=35s. The position vector was determined to be 5/3t^3 i + 1/3ln(t) j - 2t^-2 k while the acceleration vector was found to be 10t i + (t-3)/t^2 j - k. However, further verification and checking of the derivatives/integrals and cross product execution is needed.
  • #1
itr
43
0

Homework Statement


Velocity vector for a .5kg body, t=1s to t=35s, is v=5t^2 i + 3/t j – t k

WHat is the position vector? what is the angular momentum vector?what is the acceleration vector? what is torque exerted on the body?

Homework Equations


L=rxp=rxmv
T=rxf=rxma

The Attempt at a Solution


Position vector: 5/3t^3 i + 1/3ln(t) j - 2t^-2 k
Acceleration Vector: 10t i + (t-3)/t^2 j - k
I am not good in cross product so i might need verification if i did it write...granted that my vectors above are right...
L=rxp=rxmv
L=((t/6lnt)-3/2))i, ((-15/6)-(5/6t^2))j, ((5/t^6)-(5/6t^2 lnt))k.

I won't write out torque vector because it takes awhile and if i know how do do what is above right, i can manage the torque one...so please somebody review my work
 
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  • #2
All it is is checking my work...becasue there are further parts that run off of this work and i want to make sure i got this part right
 
  • #3
bold letteres are vectors
 
  • #4
PLEASE somebody check this out for me...just not sure about the derivatives/integrals and the cross product exectution
 
  • #5
Neither the position vector nor the acceleration is correct. Look after the rules of derivation and integration.

ehild
 

Related to Someone please check my simple vector algebra

What is vector algebra?

Vector algebra is a branch of mathematics that deals with the manipulation and analysis of quantities that have both magnitude and direction, known as vectors.

What are the basic operations in vector algebra?

The basic operations in vector algebra include addition, subtraction, scalar multiplication, dot product, and cross product.

How is vector algebra used in science?

Vector algebra is used in various fields of science, such as physics, engineering, and computer graphics. It helps to describe and analyze physical quantities, forces, and motion in three-dimensional space.

Can vector algebra be applied in real-world problems?

Yes, vector algebra is widely used in solving real-world problems in various fields, such as navigation, robotics, and fluid dynamics. It provides a powerful tool for understanding and solving complex mathematical problems.

What are some common mistakes made in vector algebra?

Some common mistakes made in vector algebra include forgetting to consider the direction of vectors, mixing up the order of operations, and not understanding the difference between dot and cross products. It is important to carefully follow the rules and properties of vector algebra to avoid these mistakes.

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