Models, Measurements & Vectors

Significant Figures and Measurement

Accurate measurement and reporting of significant figures are essential in physics to ensure precision and reliability of results.

• Significant Figures: The number of meaningful digits in a measurement. For example, the measurement 2.010 m has four significant figures.

• Rules: All nonzero digits are significant; zeros between nonzero digits are significant; leading zeros are not significant; trailing zeros in a decimal number are significant.

• Example: The number 0.0037010 has five significant figures.

Vector Components and Angles

Vectors are quantities with both magnitude and direction. They can be resolved into components along coordinate axes.

• Components: For a vector A with components Ax and Ay, the angle θ with the positive x-axis is given by:

• Example: If Ax = 6 units and Ay = -10 units, then θ = tan-1(-10/6) = -59°.

Motion Along a Straight Line & in a Plane

Kinematics and Acceleration

Kinematics describes the motion of objects without considering the causes. Acceleration is the rate of change of velocity.

• Constant Acceleration: If an object has velocity v = -2.00 m/s and acceleration a = -1.00 m/s2, it is speeding up (since velocity and acceleration are in the same direction).

• Equations of Motion:

• Example: A chunk of magma is launched horizontally at 208 m/s from a height of 94 m. The horizontal displacement is:

Dimensional Analysis

Dimensional analysis checks the consistency of equations by comparing units.

• Example: In the expression s = vt - 2a2, where s is distance, v is velocity, a is acceleration, and t is time, the units do not match, so the equation is not dimensionally correct.

Newton's Laws of Motion & Applications

Forces and Friction

Newton's laws describe the relationship between forces and motion. Friction is a force that opposes motion between surfaces.

• Static Friction: The force that must be overcome to start moving an object.

• Kinetic Friction: The force opposing motion once an object is moving.

• Example: For a 2.03 kg book with , N, N.

Work and Energy

Work is done when a force causes displacement. Energy is the capacity to do work.

• Work:

• Non-conservative Forces: Work done by friction, air resistance, or applied force is path dependent and always negative.

• Example: Pushing a box up a ramp:

Circular Motion & Rotational Dynamics

Circular Motion

Objects moving in a circle experience centripetal acceleration directed toward the center.

• Instantaneous Velocity: The direction of velocity is tangent to the circle at any point.

• Angular Speed: , where T is the period.

• Example: A chicken running in a circle with rad/s completes one revolution in s.

Rotational Inertia

The moment of inertia quantifies an object's resistance to changes in rotational motion.

• Moment of Inertia:

• Example: For a disk of mass 0.50 kg and radius 0.17 m, kg·m2

Angular Momentum

Angular momentum is the rotational analog of linear momentum.

• Angular Momentum:

• Example: For a disk with kg·m2 and rad/s, kg·m2/s

Work, Energy & Momentum

Kinetic Energy and Conservation

Kinetic energy is the energy of motion. Conservation of energy applies to both linear and rotational systems.

• Kinetic Energy: (linear), (rotational)

• Example: Two disks with the same angular momentum but different kinetic energies: the disk with greater kinetic energy has lower moment of inertia.

Fluid Mechanics

Pressure in Fluids

Pressure in a fluid depends on depth and density.

• Pressure:

• Example: In a container, pressure at points at the same depth is equal, regardless of shape.

• Water Density: kg/m3

• Example: Pressure at the bottom of a 2 m deep pool: Pa

Applications of Pressure

• Pressure on Immersed Objects: Pressure is greatest at the bottom of an immersed object due to greater depth.

• Minimum Pressure Calculation: For a brick weighing 50.0 N and area 0.3 m × 0.1 m, Pa

Periodic Motion

Spring and Oscillatory Motion

Springs store potential energy and can launch objects via elastic force.

• Spring Constant:

• Example: A spring with N/m compressed by 0.50 m stores J

Summary Table: Key Equations and Concepts

Additional info:

• Some questions and explanations were inferred from handwritten notes and diagrams.

• Topics covered align with chapters on kinematics, Newton's laws, work and energy, rotational motion, fluid mechanics, and periodic motion.