Willer Academy Physics Notes

Complete guide to Motion in Straight Line, Motion in a Plane, and Laws of Motion

Motion in a Straight Line

Kinematics describes motion without considering its causes.

Key Definitions

• Displacement: \(\Delta x = x_{\text{final}} - x_{\text{initial}}\)
• Average Velocity: \(v_{\text{avg}} = \frac{\Delta x}{\Delta t}\)
• Instantaneous Velocity: \(v = \frac{dx}{dt}\)
• Average Acceleration: \(a_{\text{avg}} = \frac{\Delta v}{\Delta t}\)
• Instantaneous Acceleration: \(a = \frac{dv}{dt} = \frac{d^2x}{dt^2}\)

Equations of Motion (Constant Acceleration)

1. \(v = u + at\)
2. \(s = ut + \frac{1}{2}at^2\)
3. \(v^2 = u^2 + 2as\)
4. \(s = \frac{(u + v)}{2} \times t\)

Where: \(s\) = displacement, \(u\) = initial velocity, \(v\) = final velocity, \(a\) = acceleration, \(t\) = time

SUVAT Calculator

Initial Velocity (u in m/s)

Final Velocity (v in m/s)

Acceleration (a in m/s²)

Time (t in seconds)

Displacement (s in meters)

Key Points

• The slope of a position-time graph gives velocity
• The slope of a velocity-time graph gives acceleration
• The area under a velocity-time graph gives displacement
• The area under an acceleration-time graph gives change in velocity

Motion in a Plane

Motion in two dimensions can be analyzed by resolving into two perpendicular components.

Projectile Motion

Initial Velocity: \(u\), Angle of Projection: \(\theta\)

• Initial Components: \(u_x = u \cos \theta\), \(u_y = u \sin \theta\)
• Time of Flight: \(T = \frac{2u \sin \theta}{g}\)
• Maximum Height: \(H = \frac{u^2 \sin^2 \theta}{2g}\)
• Horizontal Range: \(R = \frac{u^2 \sin 2\theta}{g}\)

Projectile Motion Calculator

Initial Velocity (m/s)

Angle of Projection (degrees)

Uniform Circular Motion

• Angular Velocity: \(\omega = \frac{\Delta \theta}{\Delta t} = \frac{2\pi}{T}\)
• Centripetal Acceleration: \(a_c = \frac{v^2}{r} = \omega^2 r\)
• Centripetal Force: \(F_c = \frac{mv^2}{r} = m\omega^2 r\)

Key Points

• Projectile motion follows a parabolic path
• The horizontal and vertical motions are independent
• Maximum range is achieved at 45°
• In circular motion, speed is constant but velocity changes due to direction change

Laws of Motion

Dynamics deals with the forces that cause motion.

Newton's Laws of Motion

1. First Law (Inertia): An object remains at rest or in uniform motion unless acted upon by a net external force.
2. Second Law: \(\sum F = ma\)
3. Third Law (Action-Reaction): For every action, there is an equal and opposite reaction.

Friction

• Static Friction: \(f_s \leq \mu_s N\)
• Kinetic Friction: \(f_k = \mu_k N\)

Momentum

• Momentum: \(\vec{p} = m\vec{v}\)
• Impulse: \(\vec{J} = \Delta \vec{p} = \vec{F} \Delta t\)
• Conservation: If \(\sum F_{\text{ext}} = 0\), then \(\sum p_{\text{initial}} = \sum p_{\text{final}}\)

Force and Acceleration Calculator

Mass (kg)

Force (N)

Problem-Solving Strategy

1. Draw a Free Body Diagram (FBD)
2. Identify all forces acting on the object
3. Choose a coordinate system
4. Resolve forces into components
5. Apply Newton's Second Law: \(\sum F_x = ma_x\), \(\sum F_y = ma_y\)
6. Solve the equations

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