Solved Example Problems for Dynamics of Circular Motion

Solved Example Problems for Centripetal force

Example 3.22

If a stone of mass 0.25 kg tied to a string executes uniform circular motion with a speed of 2 m s-1 of radius 3 m, what is the magnitude of tensional force acting on the stone?

Solution

Example 3.23

The Moon orbits the Earth once in 27.3 days in an almost circular orbit. Calculate the centripetal acceleration experienced by the Earth? (Radius of the Earth is 6.4 Ã— 106 m)

Solution

The centripetal acceleration is given by a = v2/r.  This expression explicitly depends on Moon’s speed which is non trivial. We can work with the formula

am is centripetal acceleration of the Moon due to Earth’s gravity.

ω is angular velocity.

Rm is the distance between Earth and the Moon, which is 60 times the radius of the Earth.

The centripetal acceleration of Moon towards the Earth is 0.00272 m s-2

Solved Example Problems for Vehicle on a leveled circular road

Example 3.24

Consider a circular leveled road of radius 10 m having coefficient of static friction 0.81. Three cars (A, B and C) are travelling with speed 7 ms-1, 8 m s-1 and 10 m s-1 respectively. Which car will skid when it moves in the circular level road? (g =10 m s-2)

Solution

From the safe turn condition the speed of the vehicle (v) must be less than or equal to 

The speed of car A, B and C are 7 m s-1, 8 m s-1 and 10 m s-1 respectively. The cars A and B will have safe turns. But the car C has speed 10 m s-1 while it turns which exceeds the safe turning speed. Hence, the car C will skid.

Solved Example Problems for Banking of Tracks

Example 3.25

Consider a circular road of radius 20 meter banked at an angle of 15 degree. With what speed a car has to move on the turn so that it will have safe turn?

Solution

The safe speed for the car on this road is 7.1 m s-1

Solved Example Problems for Centrifugal Force due to Rotation of the Earth

Example 3.26

Calculate the centrifugal force experienced by a man of 60 kg standing at Chennai? (Given: Latitude of Chennai is 13°

Solution

The  centrifugal force is given by Fc = mω2 R cosθ

The angular velocity (ω) of Earth = 2π/T.

where T is time period of the Earth (24 hours)

The radius of the Earth R = 6400 Km = 6400 × 103 m

Latitude of Chennai =13°

A 60 kg man experiences centrifugal force of approximately 2 Newton. But due to Earth’s gravity a man of 60 kg experiences a force =mg = 60 Ã— 9.8 = 588N. This force is very much larger than the centrifugal force.