#### Kerala PSC General Science Book Study Materials Page 6

Book's First PageOblique projectile motion (Left), Horizontal projectile motion (Middle), Projectile motion on an inclined plane (Right) Kinematic quantities of projectile motion The magnitude of the displacement: Where, r x2 y2 X axis is horizontal and Y axis is vertical. The maximum height of projectile sin θ is the component along y-axis v 0 2 sin2 () h 2g cos θ is the component along x-axis Circular Motion V0 is the initial Velocity, It is a movement of an object along the Vx is the velocity along x-axis circumference of a circle or rotation along a circular path. Vy is the velocity along y-axis It can be uniform, with constant angular g is the acceleration due to gravity and rate of rotation and constant speed, or non- uniform with a changing rate of rotation. t is the time taken. Examples of circular motion include: an artificial satellite orbiting the Earth at Acceleration constant height, a stone which is tied to a ax 0 rope and is being swung in circles. ay g Velocity in Circular Motion: Velocity d v r r dt v x v 0 cos() v y v 0 sin( ) gt Acceleration in Circular Motion: The magnitude of the velocity d v2 av v dt r v vx 2 vy 2 Where the angular rate of rotation is ω. (By rearrangement, ω = v/r.) Thus, v is a constant, Displacement and the velocity vector v also rotates with constant magnitude b, at the same angular rate At any time t, the projectile"s horizontal and ω. vertical displacement: x v 0 t cos( ) 1 y v 0 t sin( ) gt 2 2 5

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