WJEC Physics for A2: Student Bk

12 (c) Period, T , and frequency, f , of circular motion The definitions of period and frequency in the context of circular motion are essentially the same as for waves or any other periodic phenomena. The relationship between them is: frequency = 1 period f = 1 T In one revolution, the angular displacement is 2 π . We can use this to relate the period and frequency to the angular velocity, ω . ω = 2 π T and ω = 2 π f These relationships will occur in the same form for vibrational motion. We shall explore the connection at the end of this section. 3.1.2 The existence of a resultant force on an orbiting object Consider the forces on one of the fairground riders in Fig. 3.1.1. You may find it easier to use Fig. 3.1.6. Once the carousel has settled down to a steady angular velocity, the riders move in horizontal circles so they have no vertical motion. The vertical components of the forces on the riders therefore sum to zero. There are two forces, that of gravity ( mg ) and the tension force ( F ) in the support So F cos ϕ = mg i.e. F = mg cos ϕ However, there is a horizontal component to F , so there is a resultant force on the rider: F res = F sin ϕ Substituting for F from above: F res = mg sin ϕ cos ϕ But sin ϕ = tan ϕ cos ϕ ∴ F res = mg tan ϕ horizontally to the left After a half revolution, the rider will be on the left and the resultant force will be horizontally to the right. Hence there will always be a resultant force pointing to the centre of the circle. In the other examples too: • The wall of death exerts an inward force on the driver as well as a frictional force to hold him up against gravity. • The black hole and star exert attractive gravitational forces on each other. We’ll now proceed to examine the necessity for such a resultant force and how it depends upon the characteristics of the motion. The period , T , of circular motion is the time taken for one complete revolution. The frequency , f , is the number of revolutions per unit time. UNIT: Hz ≡ s −1 Terms & definitions 3.1.3 Self-test The mass of the carousel rider is 75 kg and the angle ϕ of the support cords is 50°. Calculate: (a) the tension force, F , in the cord, and (b) the resultant force on the rider. mg F axis of rotation Fig. 3.1.6 Forces on a swing carousel rider WJEC Physics for A2 Level: Unit 3