hey, very very very briefly explain uniform circular motion.
Answers
Uniform Circular Motion
Uniform motion can be defined as the motion of a body following a circular path at a constant speed. The body has a fixed central point and remains equidistant from it at any given position. When an object goes around in a circle, the description of its motion becomes interesting in many ways.
To better understand the circular motion let us look at an example. You have a ball attached to a string and you move it constantly in a circular motion. Here we observe two things:
The speed of the ball is constant. It traces a circle with a fixed centre.
At every point of its motion, the ball changes its direction. Therefore, we can say that in order to stay on a circular path, the ball has to change its direction continuously.
From the second point, an important result follows. Newton’s first law of motion tells us that there can be no acceleration without a net force. So there must be a force associated with the circular motion. In other words, for the circular motion to take place a net force has to act on the object. The change in direction is a result of a centripetal force.
Centripetal force is the force acting on a body in a circular path. It points towards the centre around which the body is moving.
As long as the ball is attached to the string, it will continue to follow the circular path. The moment the string breaks or you let go of the string, the centripetal force stops acting and the ball flies away. To study uniform circular motion, we define the following terms.
Terminologies of Uniform Circular Motion
Time Period (T)
Time period (T) is the time taken by the ball to complete one revolution. It is denoted by ‘T’. If ‘r’ is the radius of the circle of motion, then in time ‘T’ our ball covers a distance = 2πr. Let us assume the ball takes 3 seconds to complete one revolution. So T= 3 secs.
Frequency (f)
The number of revolutions our ball completes in one second is the frequency of revolution. We denote frequency by f and f = 1/T. The unit of frequency is Hertz (Hz). One Hz means one revolution per second. Here the frequency will be 1/3 Hz.
Centripetal Force
We saw earlier that a body moving in a circle changes its direction continuously. Therefore, we said that circular motion is an accelerated motion. From Newton’s laws, we know that a body can accelerate only when acted upon by some force.
In case of circular motion, this force is the centripetal force. If ‘m’ is the mass of the body, then the centripetal force on it is given by F = mv2/r; where ‘r’ is the radius of the circular orbit.
Angular Speed
We can also get an idea of how fast an object is moving in a circle if we know how fast the line joining the object to the centre of the circle is rotating. We measure this by measuring the rate at which the angle subtended at the centre changes. This quantity is ω and ω = Change in angle per unit time. Hence, ω is the Angular Speed.
The SI unit is radian / s or rad/s. For a single rotation, the change in angle is 2π and the time taken is ‘T’, therefore we can write:
ω = 2π/T = 2πν …(4)
It is usually measured in r.p.m or rotations per minute. ω = 1 r.p.m, if a body completes one rotation per minute. Also we can convert r.p.m to radians per second as i r.p.m. = 2π/60s = π/30 rad/s
Solved Examples For You
Q: A car runs at constant speed on a circular track of radius 100 m taking 62.8 s on each lap. What are the average speed and average velocity on each complete lap? (π=3.14)
velocity = 10 m/s and speed = 10 m/s
speed = 10 m/s and velocity = 0 m/s
velocity = 0 m/s and speed = 0 m/s
velocity = 10 m/s and speed = 0 m/s
Solution: B). A closer look would tell you that all the other options must be wrong, without solving it. Since in circular motion, if the particle returns to the starting position, the displacement = 0. hence, for such motion the velocity = 0 while as speed is non-zero. Now, we have circumference of each lap = 2(3.14)(100) = 628 m. Therefore, speed after each lap = 628/62.8 = 10 m/s
Uniform circular motion can be described as the motion of an object in a circle at a constant speed. As an object moves in a circle, it is constantly changing its direction. At all instances, the object is moving tangent to the circle. Since the direction of the velocity vector is the same as the direction of the object's motion, the velocity vector is directed tangent to the circle as well. The animation at the right depicts this by means of a vector arrow.