A flywheel used to prepare earthenware pots is set into rotation at 100rpm. It is in the form of a disc of mass 10kg and a radius 0.4m. A lump of clay (to be taken equivalent to a particle) of mass 1.6kg falls on it and adheres to it at a certain distance x from the center. Calculate x is the wheel now rotates at 80rpm
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In the question there is given that
• A flywheel used to prepare earthenware pots is set into rotation at 100rpm.
• It is in the form of a disc of mass 10kg and a radius 0.4m.
• A lump of clay (to be taken equivalent to a particle) of mass 1.6kg falls on it and adheres to it at a certain distance x from the center.
• and we need to Calculate x is the wheel now rotates at 80rpm
_____________________________________________
_____________________________________________
~ Let's write what is given and what we have to find
GIVEN :-
Case 1
Case 2
To FIND -
_____________________________________________
if something is freely falling or stuck on the rotating object law of conservation of angular momentum is applicable
Let's find the value of
Now , according to the law of conservation of angular momentum is
A flywheel used to prepare earthenware pots is set into rotation at 100 rpm. It is in the form of a disc of mass 10kg and radius 0.4 m. A lump of clay (to be taken equivalent to a particle) of mass 1.6 kg falls on it and adheres to it at a certain distance x from the centre. Calculate x if the wheel not rotates at 80 rpm.
Given :
Mass of flywheel = 10 kg
Radius of flywheel = 0.4 m
Mass of particle = 1.6 kg
Initial frequently = 100 rpm
Final frequency = 80 rpm
Particle is revolving in the circle of radius x m.
To Find :
The value of x.
Solution :
❖ Since no external torque acts on the whole system, angular momentum is conserved.
We know that angular momentum is measured as the product of moment of inertia and angular velocity.
Mathematically, L =I ω
❖ Moment of inertia of a disc about an axis passing through centre and perpendicular to its plane is given by,
➙ I₁ = MR²/2
➙ I₁ = 10 × (0.4)² / 2
➙ I₁ = 5 × 0.16
➙ I₁ = 0.8 kg m²
; where ω denotes angular velocity of the combined mass
Answers & Comments
A flywheel used to prepare earthenware pots is set into rotation at 100rpm. It is in the form of a disc of mass 10kg and a radius 0.4m. A lump of clay (to be taken equivalent to a particle) of mass 1.6kg falls on it and adheres to it at a certain distance x from the center. Calculate x is the wheel now rotates at 80rpm
_____________________________________________
In the question there is given that
• A flywheel used to prepare earthenware pots is set into rotation at 100rpm.
• It is in the form of a disc of mass 10kg and a radius 0.4m.
• A lump of clay (to be taken equivalent to a particle) of mass 1.6kg falls on it and adheres to it at a certain distance x from the center.
• and we need to Calculate x is the wheel now rotates at 80rpm
_____________________________________________
_____________________________________________
~ Let's write what is given and what we have to find
GIVEN :-
Case 1
Case 2
To FIND -
_____________________________________________
if something is freely falling or stuck on the rotating object law of conservation of angular momentum is applicable
Let's find the value of
Now , according to the law of conservation of angular momentum is
~ after putting the values
Question :
A flywheel used to prepare earthenware pots is set into rotation at 100 rpm. It is in the form of a disc of mass 10kg and radius 0.4 m. A lump of clay (to be taken equivalent to a particle) of mass 1.6 kg falls on it and adheres to it at a certain distance x from the centre. Calculate x if the wheel not rotates at 80 rpm.
Given :
Mass of flywheel = 10 kg
Radius of flywheel = 0.4 m
Mass of particle = 1.6 kg
Initial frequently = 100 rpm
Final frequency = 80 rpm
Particle is revolving in the circle of radius x m.
To Find :
The value of x.
Solution :
❖ Since no external torque acts on the whole system, angular momentum is conserved.
Mathematically, L = I ω
❖ Moment of inertia of a disc about an axis passing through centre and perpendicular to its plane is given by,
➙ I₁ = MR²/2
➙ I₁ = 10 × (0.4)² / 2
➙ I₁ = 5 × 0.16
➙ I₁ = 0.8 kg m²
; where ω denotes angular velocity of the combined mass
; where denotes frequency of rotation
♦ Moment of inertia of particle :