Uniform Circular Motion | Motion

2. A train is travelling at a speed of 90 km h-'. Brakes are applied so to produce a uniform acceleration of – 0.5 m s2. Find how far the train will go before it is brought to rest. 3. A trolley, while going down an inclined plane, acceleration of2 cm s². What will be its velocity 3 s after the start? 4. A racing car has a uniform acceleration of 4 m s2. What distance will it cover in 10s after Let us consider an example of the motion of a body along a closed path. Fig 8.9 (a) shows the path of an athlete along a rectangular as track ABCD. Let us assume that the athlete runs at a uniform speed on the straight parts AB, BC, CD and DA of the track. In order to keep himself on track, he quickly changes his speed at the corners. How many times will the athlete have to change his direction of motion, while he completes one round? It is clear that to move in a rectangular track once, he has to change his direction of motion four times. has an start? 5. A stone is thrown in a vertically upward direction with a velocity of 5 m sl. If the acceleration of the stone during its motion is 10 m s in the downward direction, what will be the height attained by the stone and how much time will it Now, suppose instead of a rectangular track, the athlete is running along a hexagonal shaped path ABCDEF, as shown in Fig. 8.9(b). In this situation, the athlete will have to change his direction six times while he completes one round. What if the track was not a hexagon but a regular octagon, with eight equal sides as shown by ABCDEFGH in Fig. 8.9(c)? It is observed that take to reach there? 8.6 Uniform Circular Motion as the number of sides of the track increases the athelete has to take turns more and more When the velocity of an object changes, we say that the object is accelerating. The change in the velocity could be due to change in its magnitude or the direction of the motion or both. Can you think of an example when an object does not change its magnitude of velocity but only its direction of motion? often. What would happen to the shape of the track as we go on increasing the number of sides indefinitely? If you do this you will notice that the shape of the track approaches the shape of a circle and the length of each of the sides will decrease to a point. If the athlete moves with a velocity of constant magnitude along the circular path, the only change in his velocity is due to the change in the E F direction of motion. The motion of the athlete moving along a circular path is, therefore, an example of an accelerated motion. в B (a) Rectangular track (b) Hexagonal track We know that the circumference of a circle G of radius ris given by 2r . If the athlete takes F н t seconds to go once around the circular path of radius r, the velocity v is given by E 2ur U = (8.13) D (c) Octagonal shaped track (d) A circular track When an object moves in a circular path with uniform speed, its motion is called Fig. 8.9: The motion of an athlete along closed tracks uniform circular motion. of different shapes. If you carefully note, on being released the stone moves along a straight line tangential to the circular path. This is because once the stone is released, it Activity 8.11 Take a piece of thread and tie a small piece of stone at one of its ends. Move the stone to describe a circular path with constant speed by holding the thread at the other end, as shown in continues to move along the direction it has been moving at that instant. This shows that the direction of motion changed at every point when the stone was moving along the circular path. Fig. 8.10. When an athlete throws a hammer or a discus in a sports meet, he/she holds the hammer or the discus in his/her hand and gives it a circular motion by rotating his/her own body. Once released in the desired direction, the hammer or discus moves in the Fig. 8.10: A stone describing a circular path with a velocity of constant magnitude. direction in which it was moving at the time it was released, just like the piece of stone in the activity described above. There are many more familiar examples of objects moving under uniform circular motion, such as the Now, let the stone go by releasing the thread. Can you tell the direction in which the stone moves after it is released? By repeating the activity for a few times and releasing the stone at different positions of the circular path, check whether the direction in which the motion of the moon and the earth, a satellite in a circular orbit around the earth, a cyclist on a circular track at constant speed and so on. stone moves remains the same or not.