# What is the difference between the motion of an object moving with uniform speed on a linear path and that on a circular path ?

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by ThiyaDas

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by ThiyaDas

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Let A be moving with a uniform speed v on a straight linear path.

let B be moving on a circular path of radius R, angular velocity w and time period T with a uniform speed u. u = R w. T = 2π/w

1) total length of distance travelled by A and B will be same in equal intervals.

magnitude of displacement after time t, of A is v t.

magnitude of displacement after time t of B is between 0 and 2 R only. maximum displacement is when the object is at the other end of the circle.

2) velocity vector of A is constant in magnitude and direction.

that of B is changing in direction at every instant. so is its linear momentum.

3) acceleration of A = 0

acceleration of B = m u² / R always pointed to towards the center of circle.

this is called centripetal acceleration.

4) there is no net resultant force acting on A. There is a net resultant force on B.

5) there is an angular momentum , angular velocity for B.

those are 0 for A.

let B be moving on a circular path of radius R, angular velocity w and time period T with a uniform speed u. u = R w. T = 2π/w

1) total length of distance travelled by A and B will be same in equal intervals.

magnitude of displacement after time t, of A is v t.

magnitude of displacement after time t of B is between 0 and 2 R only. maximum displacement is when the object is at the other end of the circle.

2) velocity vector of A is constant in magnitude and direction.

that of B is changing in direction at every instant. so is its linear momentum.

3) acceleration of A = 0

acceleration of B = m u² / R always pointed to towards the center of circle.

this is called centripetal acceleration.

4) there is no net resultant force acting on A. There is a net resultant force on B.

5) there is an angular momentum , angular velocity for B.

those are 0 for A.