If compared with maximum speed on a flat road we observe (v max)flat < (v max)banked. The above equation of speed suggests that no friction force is required for centripetal force. Thus substituting f = u sN in eq (i) and (ii) we get, To find vmax, we use the equation f = u sN ![]() Thus, from the figure we haveįor a safe turn, the coefficient of friction (μ s) between the tyres and the road is given by The centripetal force is induced due to the horizontal component of friction force (f) and normal force (N). Hence, the net vertical force (F y) will be zero. We know, there is no acceleration in the vertical direction of motion. It is similar to the case when a vehicle turns. The forces acting on the vehicle are shown above. The frictional effect on a motion of a vehicle can be reduced if the road is slightly banked (inclined) on the outer end. The equation can be written asĪlso check: Derivation of Centripetal AccelerationĬircular Motion on a Banked Road (Turning at Roads) Special Case: When a car takes a circular turn on a horizontal surface road, the frictional force acts as a centripetal force. Hence, at any value of μs and R, a maximum speed of a car can be achieved. ∴ v 2 ≤ μ sRg (μ s = static frictional coefficient)įrom the above expression, it is clear velocity does not depend on the mass of a car. Using the law of static friction equations (f s ≤ μ sN) and F cen = mv 2/R. This friction force opposes the motion of the car that is moving away from the circular path. This force is the frictional force (f), which is static and provides centripetal acceleration. This force is induced by the contact force between the surface of a road and the car tyres. Thus, the centripetal force required for circular motion is present along the surface of the road. Hence, the net force acting in the vertical direction will be zero. These forces are:įrom the figure, it is clear that there is no acceleration in a vertical direction. When a car moves on a level road, three primary forces are acting on the car. Where ω o is the initial angular velocity, ω is the final angular velocity, α is angular acceleration, θ is angular displacement, and t is the time taken. These circular variables are related to each other and give kinematics equations as: Windmill blade rotation is an example of uniform circular motion.Ī body executing circular motion will have angular acceleration, angular speed and angular displacement.Electrons revolving around the nucleus of an atom are an example of uniform circular motion.The motion of satellites around the planets is an example of uniform circular motion.In non-uniform motion, acceleration is given as the vector sum of radial and tangential accelerations.Ī = a r + a t Examples of Uniform Circular Motion In the case of non-uniform circular motion, there is some tangential acceleration that varies the particle’s speed. The radial acceleration (centripetal) is ω 2R.No tangential acceleration component is present i.e.The velocity of a particle is constantly varying at each instant, v = R.If any particle is undergoing uniform acceleration then If the mass of a body is ‘m’ then force is given by ![]() If no centripetal force is applied to the body it does not undergo circular motion.įor a body of mass ‘m’ undergoing circular motion, the centripetal force is given Thus, we can say a body undergoes circular motion if a force acts upon it and in the direction towards the centre of the circle or circular path of motion. According to Newton’s second law, acceleration is induced by the force in the same direction as that of force.Ĭentripetal force acting towards the centre It is given byĪ body moving with a uniform velocity (v) on a circular path with radius r possesses radial acceleration v 2/r. It is also called radial acceleration because it acts along a radius of a circular path. ![]() The acceleration act on a body undergoing circular motion whose direction is towards the centre of the circular path is called centripetal acceleration. It is important to note here, a body undergoing circular motion also has linear velocity. Angular VelocityĪngular velocity is defined as the rate of change of angular displacement (Δθ) in a circular motion. Here, ΔS is the linear displacement and ‘r’ is the radius. In the figure, Δθ is measured between position vectors rÌ and r’Ì. The figure shows the angular displacement. Angular variables are: Angular DisplacementĪngular displacement is defined as the angle subtended by a moving body at the centre of the circular path per unit of time. For example: The motion of earth around the sun is an example of circular motion.Īngular variables define the motion of a body in a circular path. The motion of an object in a circular path along the circumference of a circle or rotation along a circular path is called circular motion.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |