Mechanical Engineering

Theory of Machines – Angular Displacement Angular displacement may be defined as the angle described by a particle from one position to another with respect to time. For example, let a line OB have an inclination θ radians to the fixed line OA . If this line moves from OB to OC through an angle δθ during a short interval of time δt , then δθ is known as the angular displacement of the line OB . Since angular displacement has both magnitude and direction, it is therefore a vector quantity . Representation of Angular Displacement as a Vector In order to completely represent an angular displacement by a vector, the following three conditions must be satisfied: Direction of the axis of rotation: It is fixed by drawing a line perpendicular to the plane of rotation in which the angular displacement takes place. In other words, it is fixed along the axis of rotation. Magnitude of angular displacement: It is fixed by the length of t...

Motion of a Car Under Uniform Acceleration A car starts from rest and accelerates uniformly to a speed of 72 km/h over a distance of 500 m . Calculate the acceleration and the time taken to attain this speed. If a further acceleration raises the speed to 90 km/h in 10 seconds , find this acceleration and the further distance moved. The brakes are now applied to bring the car to rest under uniform retardation in 5 seconds . Find the distance travelled during braking. Solution Given: u = 0, v = 72 km/h = 20 m/s, s = 500 m Acceleration of the Car Let a = acceleration of the car. Using the equation: v² = u² + 2as (20)² = 0 + 2a × 500 = 1000a a = (20)² / 1000 = 0.4 m/s² Time Taken to Reach the Speed Let t = time taken. v = u + at 20 = 0 + 0.4 × t t = 20 / 0.4 = 50 s Further Acceleration from 72 km/h to 90 km/h Given: u = 20 m/s, v = 96 km/h = 25 m/s, t = 10 s Acceleration v = u + at 25 = 20 + a × 10 a = (25 − 20) / 10 = 0.5 m/s² D...