Mixing
Speed of the rotating block
Clash Royale CLAN TAG#URR8PPP
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Problem:
A block tied to a string is rotating with an angular velocity $omega$ on a frictionless table. The string passes through a hole in the center of the table. If the string is pulled and the length of the string reduces to half, find the new angular velocity of the block.
Question:
I know this question can be easily solved using conservation of angular momentum of the block because no external torque acts on it. The answer to this question will be $4 omega$.
What I wanted to know was that why would the the speed change at all? The tension due to string acts perpendicular to the direction of motion so it cannot change the angular velocity. So which force changed the angular velocity of the block??
newtonian-mechanics classical-mechanics angular-momentum angular-velocity
asked 5 hours ago
Harshit Joshi
1889
add a comment |Â
up vote
4
down vote
favorite
Problem:
A block tied to a string is rotating with an angular velocity $omega$ on a frictionless table. The string passes through a hole in the center of the table. If the string is pulled and the length of the string reduces to half, find the new angular velocity of the block.
Question:
I know this question can be easily solved using conservation of angular momentum of the block because no external torque acts on it. The answer to this question will be $4 omega$.
What I wanted to know was that why would the the speed change at all? The tension due to string acts perpendicular to the direction of motion so it cannot change the angular velocity. So which force changed the angular velocity of the block??
newtonian-mechanics classical-mechanics angular-momentum angular-velocity
asked 5 hours ago
Harshit Joshi
1889
4
If the velocity were always tangential the block would just go in a circle. For the block to spiral inwards the velocity must point slightly inwards. That means the tension and direction of motion are not perpendicular.
– John Rennie
4 hours ago
@JohnRennie Your answer does seem correct. Thanks.
– Harshit Joshi
4 hours ago
@JohnRennie. You should make that comment an answer.
– md2perpe
3 hours ago
add a comment |Â
up vote
4
down vote
favorite
up vote
4
down vote
favorite
Problem:
A block tied to a string is rotating with an angular velocity $omega$ on a frictionless table. The string passes through a hole in the center of the table. If the string is pulled and the length of the string reduces to half, find the new angular velocity of the block.
Question:
I know this question can be easily solved using conservation of angular momentum of the block because no external torque acts on it. The answer to this question will be $4 omega$.
What I wanted to know was that why would the the speed change at all? The tension due to string acts perpendicular to the direction of motion so it cannot change the angular velocity. So which force changed the angular velocity of the block??
newtonian-mechanics classical-mechanics angular-momentum angular-velocity
asked 5 hours ago
Harshit Joshi
1889
Problem:
A block tied to a string is rotating with an angular velocity $omega$ on a frictionless table. The string passes through a hole in the center of the table. If the string is pulled and the length of the string reduces to half, find the new angular velocity of the block.
Question:
I know this question can be easily solved using conservation of angular momentum of the block because no external torque acts on it. The answer to this question will be $4 omega$.
What I wanted to know was that why would the the speed change at all? The tension due to string acts perpendicular to the direction of motion so it cannot change the angular velocity. So which force changed the angular velocity of the block??
newtonian-mechanics classical-mechanics angular-momentum angular-velocity
newtonian-mechanics classical-mechanics angular-momentum angular-velocity
asked 5 hours ago
Harshit Joshi
1889
asked 5 hours ago
Harshit Joshi
1889
asked 5 hours ago
Harshit Joshi
1889
asked 5 hours ago
Harshit Joshi
1889
asked 5 hours ago
Harshit Joshi
1889
1889
4
If the velocity were always tangential the block would just go in a circle. For the block to spiral inwards the velocity must point slightly inwards. That means the tension and direction of motion are not perpendicular.
– John Rennie
4 hours ago
@JohnRennie Your answer does seem correct. Thanks.
– Harshit Joshi
4 hours ago
@JohnRennie. You should make that comment an answer.
– md2perpe
3 hours ago
add a comment |Â
4
If the velocity were always tangential the block would just go in a circle. For the block to spiral inwards the velocity must point slightly inwards. That means the tension and direction of motion are not perpendicular.
– John Rennie
4 hours ago
@JohnRennie Your answer does seem correct. Thanks.
– Harshit Joshi
4 hours ago
@JohnRennie. You should make that comment an answer.
– md2perpe
3 hours ago
4
4
If the velocity were always tangential the block would just go in a circle. For the block to spiral inwards the velocity must point slightly inwards. That means the tension and direction of motion are not perpendicular.
– John Rennie
4 hours ago
If the velocity were always tangential the block would just go in a circle. For the block to spiral inwards the velocity must point slightly inwards. That means the tension and direction of motion are not perpendicular.
– John Rennie
4 hours ago
@JohnRennie Your answer does seem correct. Thanks.
– Harshit Joshi
4 hours ago
@JohnRennie Your answer does seem correct. Thanks.
– Harshit Joshi
4 hours ago
@JohnRennie. You should make that comment an answer.
– md2perpe
3 hours ago
@JohnRennie. You should make that comment an answer.
– md2perpe
3 hours ago
add a comment |Â
3 Answers
3
active
oldest
votes
up vote
2
down vote
accepted
As the block rotates it is pulled inward via the tension in the string.
In doing so the block must move towards the hole at position $O$ which is the same direction as that of the tension $vec T$ so there must be work done $vec F cdot dvec r$ by the force which results in an increase in the kinetic energy of the block.
.
As you have pointed out the torque exerted by the tension $vec R times vec T=0$ and so the angular momentum is a conserved quantity.
answered 3 hours ago
Farcher
44.6k33388
add a comment |Â
up vote
1
down vote
When the block is rotating in a circle of radius $r$ it has a rotational kinetic energy (considering potential energy to be 0 on the table) given by $$dfrac12Iomega ²$$
According to conservation of energy, energy can neither be created nor be destroyed (forget about Einstein). The block should possess an energy equal to $$dfrac12Iomega ² + Delta W$$ What is $Delta W$ then. It is the work done by the tension on the block as it moves inwards in a circle of radius $dfracr2$.
If the block were to move with the same angular velocity it would mean loss in energy (remember conservation of energy). The block is bound to move with a higher angular velocity.
In the similar way if no external torque acts on a body it's angular momentum will be conserved (otherwise energy will be destroyed).
Velocity of an object is not due to an external force but due to it's energy. If a body at rest it set into motion by applying an impulse the body will move with a velocity $v$, because the body has been given some energy.
Hope it might help!
answered 3 hours ago
Loop Back
1209
add a comment |Â
up vote
0
down vote
Actually,
$$T=omega^2r$$
Tension actually does influence angular velocity
answered 4 hours ago
Kosh Rai
403
How do you know that? Changing the angular velocity would definitely change the tension but changing the tension will not necessarily change the angular velocity. It can also change the radius of the circle to account for the change.
– Harshit Joshi
4 hours ago
add a comment |Â
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
As the block rotates it is pulled inward via the tension in the string.
In doing so the block must move towards the hole at position $O$ which is the same direction as that of the tension $vec T$ so there must be work done $vec F cdot dvec r$ by the force which results in an increase in the kinetic energy of the block.
.
As you have pointed out the torque exerted by the tension $vec R times vec T=0$ and so the angular momentum is a conserved quantity.
answered 3 hours ago
Farcher
44.6k33388
add a comment |Â
up vote
2
down vote
accepted
As the block rotates it is pulled inward via the tension in the string.
In doing so the block must move towards the hole at position $O$ which is the same direction as that of the tension $vec T$ so there must be work done $vec F cdot dvec r$ by the force which results in an increase in the kinetic energy of the block.
.
As you have pointed out the torque exerted by the tension $vec R times vec T=0$ and so the angular momentum is a conserved quantity.
answered 3 hours ago
Farcher
44.6k33388
add a comment |Â
up vote
2
down vote
accepted
up vote
2
down vote
accepted
As the block rotates it is pulled inward via the tension in the string.
In doing so the block must move towards the hole at position $O$ which is the same direction as that of the tension $vec T$ so there must be work done $vec F cdot dvec r$ by the force which results in an increase in the kinetic energy of the block.
.
As you have pointed out the torque exerted by the tension $vec R times vec T=0$ and so the angular momentum is a conserved quantity.
answered 3 hours ago
Farcher
44.6k33388
As the block rotates it is pulled inward via the tension in the string.
In doing so the block must move towards the hole at position $O$ which is the same direction as that of the tension $vec T$ so there must be work done $vec F cdot dvec r$ by the force which results in an increase in the kinetic energy of the block.
.
As you have pointed out the torque exerted by the tension $vec R times vec T=0$ and so the angular momentum is a conserved quantity.
answered 3 hours ago
Farcher
44.6k33388
edited 3 hours ago
answered 3 hours ago
Farcher
44.6k33388
answered 3 hours ago
Farcher
44.6k33388
answered 3 hours ago
Farcher
44.6k33388
44.6k33388
add a comment |Â
add a comment |Â
up vote
1
down vote
When the block is rotating in a circle of radius $r$ it has a rotational kinetic energy (considering potential energy to be 0 on the table) given by $$dfrac12Iomega ²$$
According to conservation of energy, energy can neither be created nor be destroyed (forget about Einstein). The block should possess an energy equal to $$dfrac12Iomega ² + Delta W$$ What is $Delta W$ then. It is the work done by the tension on the block as it moves inwards in a circle of radius $dfracr2$.
If the block were to move with the same angular velocity it would mean loss in energy (remember conservation of energy). The block is bound to move with a higher angular velocity.
In the similar way if no external torque acts on a body it's angular momentum will be conserved (otherwise energy will be destroyed).
Velocity of an object is not due to an external force but due to it's energy. If a body at rest it set into motion by applying an impulse the body will move with a velocity $v$, because the body has been given some energy.
Hope it might help!
answered 3 hours ago
Loop Back
1209
add a comment |Â
up vote
1
down vote
When the block is rotating in a circle of radius $r$ it has a rotational kinetic energy (considering potential energy to be 0 on the table) given by $$dfrac12Iomega ²$$
According to conservation of energy, energy can neither be created nor be destroyed (forget about Einstein). The block should possess an energy equal to $$dfrac12Iomega ² + Delta W$$ What is $Delta W$ then. It is the work done by the tension on the block as it moves inwards in a circle of radius $dfracr2$.
If the block were to move with the same angular velocity it would mean loss in energy (remember conservation of energy). The block is bound to move with a higher angular velocity.
In the similar way if no external torque acts on a body it's angular momentum will be conserved (otherwise energy will be destroyed).
Velocity of an object is not due to an external force but due to it's energy. If a body at rest it set into motion by applying an impulse the body will move with a velocity $v$, because the body has been given some energy.
Hope it might help!
answered 3 hours ago
Loop Back
1209
add a comment |Â
up vote
1
down vote
up vote
1
down vote
When the block is rotating in a circle of radius $r$ it has a rotational kinetic energy (considering potential energy to be 0 on the table) given by $$dfrac12Iomega ²$$
According to conservation of energy, energy can neither be created nor be destroyed (forget about Einstein). The block should possess an energy equal to $$dfrac12Iomega ² + Delta W$$ What is $Delta W$ then. It is the work done by the tension on the block as it moves inwards in a circle of radius $dfracr2$.
If the block were to move with the same angular velocity it would mean loss in energy (remember conservation of energy). The block is bound to move with a higher angular velocity.
In the similar way if no external torque acts on a body it's angular momentum will be conserved (otherwise energy will be destroyed).
Velocity of an object is not due to an external force but due to it's energy. If a body at rest it set into motion by applying an impulse the body will move with a velocity $v$, because the body has been given some energy.
Hope it might help!
answered 3 hours ago
Loop Back
1209
When the block is rotating in a circle of radius $r$ it has a rotational kinetic energy (considering potential energy to be 0 on the table) given by $$dfrac12Iomega ²$$
According to conservation of energy, energy can neither be created nor be destroyed (forget about Einstein). The block should possess an energy equal to $$dfrac12Iomega ² + Delta W$$ What is $Delta W$ then. It is the work done by the tension on the block as it moves inwards in a circle of radius $dfracr2$.
If the block were to move with the same angular velocity it would mean loss in energy (remember conservation of energy). The block is bound to move with a higher angular velocity.
In the similar way if no external torque acts on a body it's angular momentum will be conserved (otherwise energy will be destroyed).
Velocity of an object is not due to an external force but due to it's energy. If a body at rest it set into motion by applying an impulse the body will move with a velocity $v$, because the body has been given some energy.
Hope it might help!
answered 3 hours ago
Loop Back
1209
answered 3 hours ago
Loop Back
1209
answered 3 hours ago
Loop Back
1209
answered 3 hours ago
Loop Back
1209
1209
add a comment |Â
add a comment |Â
up vote
0
down vote
Actually,
$$T=omega^2r$$
Tension actually does influence angular velocity
answered 4 hours ago
Kosh Rai
403
How do you know that? Changing the angular velocity would definitely change the tension but changing the tension will not necessarily change the angular velocity. It can also change the radius of the circle to account for the change.
– Harshit Joshi
4 hours ago
add a comment |Â
up vote
0
down vote
Actually,
$$T=omega^2r$$
Tension actually does influence angular velocity
answered 4 hours ago
Kosh Rai
403
How do you know that? Changing the angular velocity would definitely change the tension but changing the tension will not necessarily change the angular velocity. It can also change the radius of the circle to account for the change.
– Harshit Joshi
4 hours ago
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Actually,
$$T=omega^2r$$
Tension actually does influence angular velocity
answered 4 hours ago
Kosh Rai
403
Actually,
$$T=omega^2r$$
Tension actually does influence angular velocity
answered 4 hours ago
Kosh Rai
403
answered 4 hours ago
Kosh Rai
403
answered 4 hours ago
Kosh Rai
403
answered 4 hours ago
Kosh Rai
403
403
How do you know that? Changing the angular velocity would definitely change the tension but changing the tension will not necessarily change the angular velocity. It can also change the radius of the circle to account for the change.
– Harshit Joshi
4 hours ago
add a comment |Â
How do you know that? Changing the angular velocity would definitely change the tension but changing the tension will not necessarily change the angular velocity. It can also change the radius of the circle to account for the change.
– Harshit Joshi
4 hours ago
How do you know that? Changing the angular velocity would definitely change the tension but changing the tension will not necessarily change the angular velocity. It can also change the radius of the circle to account for the change.
– Harshit Joshi
4 hours ago
How do you know that? Changing the angular velocity would definitely change the tension but changing the tension will not necessarily change the angular velocity. It can also change the radius of the circle to account for the change.
– Harshit Joshi
4 hours ago
add a comment |Â
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4
If the velocity were always tangential the block would just go in a circle. For the block to spiral inwards the velocity must point slightly inwards. That means the tension and direction of motion are not perpendicular.
– John Rennie
4 hours ago
@JohnRennie Your answer does seem correct. Thanks.
– Harshit Joshi
4 hours ago
@JohnRennie. You should make that comment an answer.
– md2perpe
3 hours ago