WJEC Physics for A2: Study and Rev Guide

3.1.3 Centripetal acceleration A body moving at constant speed around a circular path is accelerating, because its velocity is always changing (in direction). The change in velocity over the arc AB is found using the vector diagram, which is based on: velocity at B – velocity at A = velocity at B + (–velocity at A ) v A v B v B – v A – v A ν B O A B Fig. 3.1.4 Velocity change for body on a circular path As the vector diagram suggests, the change in velocity, and hence the acceleration, is centripetal : always directed towards the circle centre. For a body moving at speed v (and angular velocity w ) in a circle of radius r , the magnitude of the acceleration is a = v 2 r or, equivalently, a = r w 2 Example The London Eye is a giant wheel rotating at a constant angular velocity. Each revolution takes 30 minutes. Calculate the acceleration of a point on the wheel 60m from its centre. Answer w = 2 p T = 2 p 30 × 60 s ; a = r w 2 = 60m × 2 p 30 × 60 s 2 = 7.3 × 10 −4 ms −2 Centripetal force A body can’t move in a circle at constant speed without having a resultant force acting on it towards the centre of the circle, to give it the centripetal acceleration. Using Newton’s second law, F res = ma so in this case F res = m v 2 r and F res = mr w 2 Example (a) (b) (c) θ θ θ m mg S F res = mr ω 2 mg S Fig. 3.1.5 ‘Conical pendulum’ and the forces on its bob Pointer Check that the units of v 2 r are those of acceleration. Pointer You should show, using v = r w , that a = v 2 r and a = r w 2 really are equivalent. E A train is travelling at 18.0 m s −1 on a curved section of track. The curve is an arc of a circle of radius 120 m . Calculate the train’s acceleration. QUICKFIRE QUICKFIRE QUICKFIRE F A carriage of the train in Quickfire 4 has a mass of 36000kg . Find the centripetal force on it. What external ‘object’ exerts this force? QUICKFIRE QUICKFIRE 10 A Level Physics: Study and Revision Guide