What are the differences between scalar and vector quantities?
Scalar: Magnitude only (e.g., speed, mass). Vector: Magnitude and direction (e.g., velocity, force).
What are the differences between sine and cosine in vector resolution?
Sine: Used for the opposite side (usually y-component). Cosine: Used for the adjacent side (usually x-component).
Difference between static and kinetic friction?
Static friction: Prevents motion from starting. Kinetic friction: Opposes motion that is already occurring.
Difference between displacement and distance?
Displacement: Change in position (vector). Distance: Total length traveled (scalar).
Difference between speed and velocity?
Speed: How fast an object is moving (scalar). Velocity: How fast and in what direction an object is moving (vector).
What is the effect of increasing the angle of a projectile launch (up to 45 degrees) on its range?
Increases the range.
What is the effect of increasing the magnitude of a force applied to an object?
Increases the object's acceleration (Newton's Second Law).
What happens when the net force on an object is zero?
The object remains at rest or continues to move at a constant velocity (Newton's First Law).
What is the effect of increasing the coefficient of friction between two surfaces?
Increases the frictional force between the surfaces.
What happens to the vertical component of velocity of a projectile at its maximum height?
It becomes zero.
How do you find the magnitude of a resultant vector from perpendicular components?
Use the Pythagorean theorem: $R = \sqrt{A_x^2 + A_y^2}$.
How do you resolve a vector into its x and y components?
Use trigonometry: $A_x = A \cos \theta$ and $A_y = A \sin \theta$, where $\theta$ is the angle with respect to the positive x-axis.
Steps to add vectors A and B to find resultant vector R?
1. Resolve A and B into x and y components. 2. Add the x-components: $R_x = A_x + B_x$. 3. Add the y-components: $R_y = A_y + B_y$. 4. Find the magnitude of R: $R = \sqrt{R_x^2 + R_y^2}$. 5. Find the direction of R: $\theta = \tan^{-1}(R_y / R_x)$.
Steps to solve a 2D kinematics problem involving projectile motion?
1. Resolve initial velocity into horizontal and vertical components. 2. Analyze horizontal motion (constant velocity). 3. Analyze vertical motion (constant acceleration due to gravity). 4. Use kinematic equations to find unknowns (time, range, max height).
Steps to draw a free-body diagram?
1. Identify the object of interest. 2. Represent the object as a point. 3. Draw and label all forces acting on the object (gravity, normal force, friction, applied forces). 4. Ensure forces are drawn in the correct direction.
Steps to calculate the net force on an object on an inclined plane?
1. Draw a free-body diagram. 2. Resolve gravitational force into components parallel and perpendicular to the incline. 3. Calculate the normal force. 4. Calculate the frictional force (if any). 5. Sum the forces along the incline to find the net force.
