This is a topic that is connected to Simple harmonic motion.
Circular motion can be defined as the motion of a body with a constant speed in a circular manner. Examples of circular motion are motion of a wheel, A stone tied to a rope and being swung, a car turning round a curve etc.
It is important to know that in a circular motion, the direction of motion at any instant is the direction of the tangent at that point. This can be seen in the diagram below.
Things to note about a body moving in a circular manner
- The speed is constant
- The velocity is not constant because the body is changing direction.
- The acceleration is not constant
- The acceleration is directed towards the centre (centripetal acceleration)
- No work is done on the body.
- The direction of the centripetal acceleration is perpendicular to the velocity
Centripetal Force and Centrifugal force
When a body is moving in a circular manner, it is directed towards the centre with the help of a force which is known as Centripetal Force.
Centripetal Force is a force that keeps a body moving in a circular manner. It is also the force that direct the body towards the centre. Centrifugal Force is the force that direct the body away from the centre.
Centripetal Force can be calculated by using this formula.
Where f= centripetal force in Newton
m= mass of the body in kilogram
r = radius in metres
We can also derive formula for centripetal acceleration.
Let's take some questions on this
- An object of mass 2kg moves with a velocity of 10ms⁻¹ round a circle of radius 4m.Calculate the centripetal force on the object.
Solution
m= 2kg, v=10ms⁻¹ , r=4m
- A force F is required to keep a 5kg mass moving round a cycle of radius 3.5m at a speed of 7m/s What is the speed, if the force is tripled?
Solution
- A gramophone record takes 5s to reach its constant angular velocity of 4π rad/s from rest. Find its constant angular acceleration.
Solution
t=5sec, w= 4π rad/s, 𑁛=?
- What is the maximum velocity of a particle undergoing circular motion such that the radius of the path is 75cm and its moving at 100 r.p.m
Solution
Exercises
- A car of mass 1500 kg goes round a circular curve of radius 50m at a speed of 40ms⁻¹. The magnitude of the centripetal force on the car is
- A piece of stone attached to one end of a string is whirled round in a horizontal circle and the string suddenly cuts. The stone will fly off in a direction (a)tangential to the circular path (b)parallel to the circular path (c)perpendicular to the circular path (d)towards the centre of the circle
- A body of mass 400g moving round a circular track of radius 50cm with a velocity of 12m/s. The centripetal force on the object is ..
- If a wheel 1.2m in a diameter rotates at one revolution per second, calculate the velocity of the wheel.
Answer the questions and write your answers in the comment section below