1) Graphically. Draw an arrow for the force, and measure the vertical and horizontal components.
2) Use trigonometry. The x-component is the length of the vector times the cosine of the angle, while the y-component is the length of the vector times the sine of the angle.
3) Use the polar-to-rectangular conversion on your scientific calculator. This is the fastest method, but the details are a bit complicated (since the calculator needs to return two values), and vary from one calculator to another. Check your calculator's manual.
lved in its rectangular components
certainly. The force vector can be resolved into one component parallel to the motion of the object under force and another component perpendicular to the motion. The parallel component does the work; the perpendicular component does no work
No. At least not by the force that's perpendicular to the motion. When you push a baby stroller (or a car), you do work, but the force of gravity, downward and perpendicular to the motion, doesn't.
This is usually 90 degrees. They work together in reciprocal motion even though all of the components are of a sinusoidal nature.
Because work done is equal to the force times the distance travelled IN THE DIRECTION of the force. Distance travelled in an oblique direction can be decomposed into two components: s*cos(x) in the direction of the force and s*sin(x) in a direction perpendicular to it (where x is the angle between the force and the resultant motion). Motion in a perpendicular direction is NOT work done by the force, which leaves s*cos(x). Multiply by the force (as required) and you have your answer.
The force associated with Torque T is always perpendicular to the torque motion, T=FxR.
lved in its rectangular components
An unlimited amount
Nonperpendicular vectors need to be resolved into components because the Pythagorean theorem and the tangent function can be applied only to right triangles.
Force can be resolved into horizontal and vertical components using vector analysis. However stress cannot be resolved into horizontal and vertical components using vector analysis since it is not a vector but a tensor of second order.
Vector addition does not follow the familiar rules of addition as applied to addition of numbers. However, if vectors are resolved into their components, the rules of addition do apply for these components. There is a further advantage when vectors are resolved along orthogonal (mutually perpendicular) directions. A vector has no effect in a direction perpendicular to its own direction.
certainly. The force vector can be resolved into one component parallel to the motion of the object under force and another component perpendicular to the motion. The parallel component does the work; the perpendicular component does no work
Helical motion refers to the motion of an object moving along a helix, which is a three-dimensional spiral shape. This type of motion combines linear and rotational movements, resulting in a path that moves both along an axis and in a circular pattern simultaneously. Helical motion is commonly observed in various mechanical systems and natural phenomena.
A vector can be resolved into infinitely many sets of components in both 2D and 3D space.
perpendicular
When a ball collides with a wall, at an angle θ say, the impulse exerted on the ball is perpendicular to the wall and causes a change in the momentum of the ball in that direction; it does not however affect the momentum parallel to the wall. Therefore, if the approach velocity of the sphere is resolved into components parallel and perpendicular to the wall, one of these components is changed by the impact and the other remains unchanged.
No. At least not by the force that's perpendicular to the motion. When you push a baby stroller (or a car), you do work, but the force of gravity, downward and perpendicular to the motion, doesn't.
Lift is the force that acts upwards, perpendicular to the chord of the wing. Thrust is the force acting perpendicular to the propeller disc.