Physics XI - Chapter 04: Motion in a Plane
Chapter-wise Multiple Choice Questions with Instant Feedback
Quick Revision Box
- Scalar Quantities: Magnitude only (distance, speed, mass). Vector Quantities: Magnitude and direction (displacement, velocity, acceleration, force).
- Vector Addition: Triangle law, parallelogram law, and component method for adding vectors.
- Projectile Motion: Two-dimensional motion under constant acceleration (gravity).
- Key Projectile Equations:
- Time of flight: T = (2u sinθ)/g
- Maximum height: H = (u² sin²θ)/(2g)
- Horizontal range: R = (u² sin2θ)/g
- Equation of path: y = x tanθ - (gx²)/(2u² cos²θ)
- Maximum Range: Occurs at θ = 45°, R_max = u²/g
- Complementary Angles: Projectiles fired at angles θ and (90°-θ) have same range.
- At Highest Point: Vertical velocity = 0, Acceleration = g downward, Speed = u cosθ
- Uniform Circular Motion:
- Constant speed, continuously changing velocity
- Centripetal acceleration: a = v²/r = ω²r
- Angular velocity: ω = 2π/T = 2πf
- Relation: v = rω
- Centripetal Force: F = mv²/r = mω²r, always directed towards center
- Relative Velocity: v_AB = v_A - v_B (velocity of A relative to B)
- Non-uniform Circular Motion: Has both tangential and centripetal acceleration components
- Radius of Curvature: R = v²/a_normal, where a_normal is component of acceleration perpendicular to velocity
- Projectile on Inclined Plane: Range maximum when θ = π/4 - β/2, where β is incline angle
- Important Values: sin0°=0, sin30°=1/2, sin37°=3/5, sin45°=1/√2, sin53°=4/5, sin60°=√3/2, sin90°=1
Basic Level Questions
Chapter Summary
This chapter extends our understanding of motion from one dimension to two dimensions, introducing us to the powerful concept of vectors - quantities that have both magnitude and direction. We learn how to add and resolve vectors using various methods, which becomes crucial for analyzing complex motions. The core of this chapter revolves around two fundamental types of motion: projectile motion and circular motion, each with its unique characteristics and mathematical descriptions.
Projectile motion demonstrates the beautiful principle of independence of motions - the horizontal motion with constant velocity and vertical motion with constant acceleration due to gravity combine to form a parabolic path. The key parameters - time of flight, maximum height, and horizontal range - can be precisely calculated using the derived equations. Circular motion introduces us to the concept of centripetal acceleration, which is essential for any object moving along a curved path, even when its speed is constant. We discover that in uniform circular motion, while speed remains constant, velocity continuously changes due to the changing direction, resulting in centripetal acceleration directed towards the center.
Mastering this chapter provides the foundation for understanding more complex motions in physics and engineering. The concepts of relative velocity help us analyze motion from different reference frames, while the mathematical treatment of projectile and circular motions develops our problem-solving skills for real-world scenarios like satellite motion, planetary orbits, and various sports dynamics. Remember to pay special attention to vector operations and the conditions under which different equations are applicable.