Question

Take a piece of thread 1m long and tie a small piece of stone at one of its ends. Move the stoneto describe a circular path with constant speed by holding the thread at the other end, as
Answer these questions as per your understanding

i. How much distance will the stone cover in
one rotation?

ii. What will be the displacement of the stone
after one cycle of motion?

iii. Does stone changes it's direction of velocity at
every instant?

iv. What is the direction of acceleration?

v. Can we have a circular motion without
acceleration?

Answer 1

Answer:

Part i)

Distance moved by stone is one complete revolution is

$d = 6.28 m$

Part ii)

displacement = ZERO

Part iii)

Direction of velocity of the stone is tangential to the path So it is changing at each instant of time

Part iv)

Direction of acceleration of the stone is always towards the center of the circle this is why it is known as centripetal acceleration

Part v)

Since the direction of velocity is changing at each instant of time so circular motion without acceleration is not possible

Explanation:

Part i)

Since the stone is moving in circular path so distance moved by it in one complete revolution is same as the circumference of the circle

So we have

$d = 2\pi R$

here radius is same as the length of the string so R = 1 m

$d = 2\pi(1)$

$d = 6.28 m$

Part ii)

Since the initial and final position of the stone is same after one complete revolution

So the displacement = ZERO

Part iii)

Direction of velocity of the stone is tangential to the path So it is changing at each instant of time

Part iv)

Direction of acceleration of the stone is always towards the center of the circle this is why it is known as centripetal acceleration

Part v)

Since the direction of velocity is changing at each instant of time so circular motion without acceleration is not possible

#Learn

Topic : Circular Motion

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