What is the relationship between the torque and position vectors?

In summary, a 5.0 kg object with a position vector of r= i^+2j^+3k^ meters and an acceleration of a=5i^+6j^-7k^ m/s^2 has a torque of T=-10(381)^1/2 around the origin of the coordinate system. It can be proven that the torque is perpendicular to the position vector r by taking the dot product of the two vectors, which results in 0.
  • #1
nameVoid
241
0
A 5.0 kg object at r= i^+2j^+3k^ meters has an acceleration a=5i^+6j^-7k^ m/s^2

a)what is the objects torque around the origin of the cordinate system
b)prove that the torque is perpendicular to the position vector r

a)
t^=rXma=-10<16,-11,2>
t=-10(381)^1/2

b)
<1,2,3>*<16,-11,2>=0
 
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  • #2
Do you have a question? What you have looks fine to me.
 
  • #3
I was marked wrong for that on an exam
 
  • #4
The torque T is a vector, and I get what you get.

The magnitude of the torque (which wasn't asked for), |T| is +10*sqrt(381), not -10sqrt(381) as you had.

The dot product of <1, 2, 3> and 10<-16, 11, -2> is 0, so the two vectors are perpendicular. Maybe you were supposed to prove that the torque and position vectors are perpendicular in general, not just for the values in this problem.
 

FAQ: What is the relationship between the torque and position vectors?

What is the cross product torque?

The cross product torque, also known as the vector or moment of torque, is a mathematical concept used to describe the rotational force exerted on an object. It is calculated by taking the cross product of two vectors - the position vector and the force vector - and multiplying it by the sine of the angle between them.

How is cross product torque different from regular torque?

The main difference between cross product torque and regular torque is that cross product torque takes into account the direction of the force vector, while regular torque only considers the magnitude of the force. Cross product torque is a vector quantity, meaning it has both magnitude and direction, while regular torque is a scalar quantity with only magnitude.

What is the formula for calculating cross product torque?

The formula for calculating cross product torque is: τ = r x F, where τ is the cross product torque, r is the position vector, and F is the force vector. This formula can also be written as τ = rFsinθ, where θ is the angle between the position and force vectors.

What are some real-world examples of cross product torque?

Cross product torque can be seen in many everyday situations, such as opening a door, tightening a bolt, or using a wrench to turn a nut. In all of these cases, a force is applied at a certain distance from the axis of rotation, resulting in a rotational force or torque.

How is cross product torque used in physics and engineering?

Cross product torque is an important concept in both physics and engineering, as it is used to describe the rotational motion of objects. It is used in the design and analysis of machines and structures, as well as in understanding the movement of planets and stars. In physics, it is a key component of the equations of motion for rotational systems.

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