Did you know?
Did you know that when a stone is whirled at the end of a rope, it undergoes angular motion and completes revolutions? In a particular case, a stone on a 30cm long rope completes 10 full revolutions in just 2 seconds. This interesting scenario allows us to find some key properties.
First, we can determine the angular velocity, which measures how quickly the stone's position changes as it revolves. To calculate this, we divide the number of revolutions (10) by the time taken (2 seconds). In this case, the angular velocity is 5 radians per second, indicating that the stone sweeps through an angle of 5 radians in one second.
Additionally, we can explore the linear speed of the stone, which describes its velocity along its circular path. To find this, we multiply the angular velocity (5 radians per second) by the radius of the path (30cm or 0.3 meters). Thus, the linear speed of the stone is 1.5 meters per second, meaning it travels a distance of 1.5 meters along the circular path in 1 second.
Lastly, if we want to determine the total distance covered by the stone in these 2 seconds, we multiply the linear speed (1.5 meters per second) by the total time (2 seconds). Therefore, the stone covers a distance of 3 meters during this entire duration.
This scenario not only showcases the concept of angular velocity and linear speed, but it also provides a practical application where we can measure distances and calculate the motion of objects in circular paths.
