CIRCULAR MOTION. We will study the mechanics. (kinematics and dynamics) of a body moving in a circle or a curved path with a constant velocity. Apply your knowledge of centripetal acceleration and centripetal force to the solution of problems in circular motion. •• Define and apply concepts of frequency . Chapter 5 - Uniform Circular Motion. • Velocity: if constant speed (magnitude), but changes direction – acceleration. • And if there is acceleration, there is a net.

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We shall describe the kinematics of circular motion, the position, velocity, and acceleration, as a special case of two-dimensional motion. You place a beetle on a uniformly rotating record. (a) Is the beetle's tangential velocity different or the same at different radial positions? (b)Is the beetle's angular. PDF | An extraordinarily simple and transparent derivation of the formula for the acceleration that occurs in uniform circular motion is presented.

A bob is attached to one end of a string other end of which is fixed at peg A. The bob is taken to a position where string makes an angle of with the horizontal. On the circular path of the bob in vertical plane there is a peg B at a symmetrical position with respect to the position of release as shown in the figure. COM India's No. A section of fixed smooth circular track of radius R in vertical plane is shown in the figure. A block is released from position A and leaves the track at B. Its kinetic energy varies as a function of time as : K. A small cube with mass M starts at rest at point 1 at a height 4R, where R is the radius of the circular part of the track. The cube slides down the frictionless track and around the loop. The tube AC forms a quarter circle in a vertical plane.

Exam Hint: All bodies moving in a circle are accelerating see later but they only have angular acceleration if their angular velocity changes. Instead of giving angular speed in rad s-1 , questions may give you angular speed in revolutions per second; you may also be given the period of the motion — the time required to complete one full circle. You need to convert to radians per second before using any formulae! To convert: Every body continues at rest or with constant velocity unless acted upon by a resultant force Since velocity is a vector quantity, possessing both magnitude the speed and direction, if velocity is constant, then both the speed and direction of motion must be constant.

In circular motion, although the speed may be constant, the velocity is continually changing direction. At any point on the circular path, the velocity is along the tangent to the circle at that point — it is at right angles to a line joining the moving particle to the centre of the circle Since the velocity of a body performing circular motion is changing, the body must be subject to a force.

If the force acting on the body had a component parallel to the velocity, this would increase or decrease the speed of the body. So, if the speed is constant, the force must be perpendicular to the velocity at all times. Therefore we can conclude that: A body moving in a circular path experiences a force directed towards the centre of the circle.

This is known as centripetal force. Where does the centripetal force come from? Some examples of forces producing circular motion are shown below; others will be encountered in other contexts later in the course. This happens because the force s providing the centripetal force vanish as with the string breaking , or become insufficient to hold the body to the circular path.

What happens after leaving the circular path After leaving the circular path, the body will initially go off at a tangent: Its motion will then, of course, be governed by the forces still acting on it eg gravity. Why bodies may leave the circular path To see why this happens, we need to return to centripetal force: If the tension is too great, the string will break.

The higher the speed of the body, the higher the centripetal force is required to be.

So the string may break if the body is being swung too fast. So if the speed is too high, the friction may not provide sufficient centripetal force, and the car will skid.

Typical Exam Question A car travels along a level road round a curve of radius m. This means that the size of the centripetal force on the body will also vary. Here, the key approach is: Draw a diagram, showing all the forces. Use conservation of mechanical energy to find the speed at any point.

A particle is attached to an end of a rigid rod. The other end of the rod is hinged and the rod rotates always remaining horizontal. Its angular speed is increasing at constant rate.

The mass of the particle is 'm'. The force exerted by the rod on the particle is F , then : A F mg C The angle between F and horizontal plane decreases.

D The angle between F and the rod decreases. A heavy particle is tied to the end A of a string of length 1. Its other end O is fixed. It revolves as a conical pendulum with the string making 60o with the vertical. A simple pendulum of length L and mass bob M is oscillating in a plane about a vertical line between angular limits and.

A machine, in an amusement park, consists of a cage at the end of one arm, hinged at O. The cage is so attached that the man of weight w standing on a weighing machine, inside the cage, is always vertical.

Then which of the following is correct A the reading of his weight on the machine is the same at all positions B the weight reading at A is greater than the weight reading at E by 2 w. A car of mass M is travelling on a horizontal circular path of radius r.

A particle is moving with constant angular acceleration in a circular path of radius 3 m. A particle P is moving on a circle under the action of only one force acting always towards fixed point O on 2 the circumference. A ball is held at rest in position A by two light cords as in figure. The horizontal cord is cut a n d the ball starts swinging as pendulum.

A particle is placed on the surface of the earth such that its position vector w. What should be the time period of the rotation of earth about its own axis so that the weight of the object measured by a weighing machine at that position is half of its real weight. Figure shows the direction of total acceleration and velocity of a particle moving clockwise in a circle of radius 2. A table with smooth horizontal surface is fixed in a cabin that rotates with a uniform angular velocity in a circular path of radius R figure.

The groove makes an angle with the radius OA of the circle in which the cabin rotates. A small particle is kept at the point A in the groove and is released to move along AB. Find the time taken by the particle to reach the point B.

India's No. A particle is travelling in a circular path of radius 4m. Particle then continues to move with attained speed.

Calculate a angular acceleration of the particle, b tangential velocity of the particle as a function of time. Determine the tangential and normal accelerations of the stone in 1 second after it begins to move. A particle moves in a circle of radius R with a constant speed v.