The power reached to a system which is rotating in a uniform motion about a particular axle in a given time period is the torque times the angular velocity. Angular velocity and torque inversely proportional with each other.
Angular velocity is the vector expression of the motion of the rotation which represents how fast a substance can revolves or rotates compare to another point. Torque can be explained as the measurement of the force which responsible for rotation of a substance about an axle.
In the simple word, the meaning of the angular velocity is the rate of the time at which a substance revolves, rotates regarding an axle or at which the angular displacement between two bodies variations.
The dimensional formula for the angular velocity is, M^0L^0T^-^1 where, M is denoted as the mass of the matter, L is denoted as length of the matter and T is denoted as time taken by the matter.
The S.I. unit for the angular velocity is radians per second (rad/s). The point of compass for the angular velocity is straight way perpendicular to the plane of the rotation. The dimensional formula for the torque is ML^2T^-^2 .
The S.I. unit for the torque is Newton meter. The torque term as, moment of force, force, rotational force which is depends upon the bounds of the study.
Is torque the same as angular velocity?
Angular velocity is representing with the help of Greek letter omega (\omega), and torque is representing with the help of \tau.
No, torque and angular velocity both are the different terms. The term torque is the measure of shortest force. The torque refers to the strength of a force to generate change in the motion of the rotational of a matter. The meaning of the angular velocity is the rate of the time at which a substance revolves, rotates regarding an axle or at which the angular displacement between two bodies variations.
For a particular matter revolution about an axle, each dot on the matter has the similar amount of angular velocity. But points major from the axle of rotation move at several tangential velocities than points closer to the axle of revolution.
Another term for the angular velocity is angular frequency vector and rotational velocity.
Image Credit – Wikipedia
Does torque depend on angular velocity?
If the value of torque increases then the value of angular velocity decreases in the same way if the value of torque is decrease then the value of angular velocity is increase.
The physical property torque is depending upon the angular velocity. The angular velocity or angular speed is inversely proportional with the physical property of the torque. The torque for a matter which is rotate in a motion can be express as the proportion of power and angular velocity.
What is the relationship between torque and angular velocity?
Torque is directly proportional with the power. Means the value of torque is increase then the value of power is also increases and when the value is decrease in that case the value of power will be also decreases.
The relationship between the torque and angular velocity is indirectly proportional with each other, means if the value of torque increases then the value of angular velocity decreases in the same way if the value of torque is decrease then the value of angular velocity is increase.
Torque is the cyclic identity of shortest force. In the other hand the speed is used to estimate the distance travelled in a certain time. For a rotating object torque can be expressed as the proportion of the physical property of power and the physical property of angular velocity.
Formula for the torque and angular velocity or angular speed:-
The formula for the torque and angular velocity or angular speed is,
Torque = \frac{Power}{Speed}
\tau = \frac{P} {\omega}
Derivation the formula for the torque and angular velocity or angular speed:-
The derivation of the formula for the torque and angular velocity or angular speed is,
\tau is denoted as Torque.
P denoted as the power
\omega denoted as angular velocity or angular speed.
As per rearranging the above equation the value of angular velocity or torque can be estimate. After observing the equation the relation between the torque and power or the relationship between torque and angular velocity easily can be written.
How to find angular velocity from torque?
Torque is not energy. Torque is vector expression. The direction of the torque vector depends on the direction of the force on the axle.
For the case of the motion of the rotation to explain the relationship in between the power and torque, assimilate the linear equivalent. The linear displacement can be explained as; the distance travelled at the surrounding if the revolution and is estimate by the product of the radius and covered angle.
Linear distance can be written as the product of the time and linear velocity.
The expression for the linear distance is,
Linear distance = Radius \times Angular velocity \times Time
Torque can be explained as the measurement of the force which responsible for rotation of a substance about an axle.
Torque = Force \time Radius
Force = \frac{Torque}{Radius}
Power = \frac{Force \times Linear Distance}{Time}
Power = \frac{\frac{Torque}{Radius} \times Angular velocity \times Time}{Time}
Power = Torque \times Angular velocity
Torque = \frac{Power}{Angular velocity}
In this way the angular velocity can be estimate from the torque.
Angular velocity and torque graph:
In the angular and torque graph in vertical portion torque is plotted and and horizontally angular velocity is plotted.
Problem statement with solution:-1
A boy plays with his toy. When the boy is spinning his toy that time the he applied the power on his toy about 15 Watt. Now the toy starts to spinning at the rate of 12 radians per second.
Now estimate the amount of torque.
Solution:-
Given data are,
Power (P) = 15 Watt.
Angular velocity (\omega) = 12 radians per second
Need to calculate the value of torque (\tau) =?
We know,
The formula for the torque and angular velocity or angular speed is,
Torque = \frac{Power}{Speed}
\tau = \frac{P} {\omega}
Where,
\tau is denoted as Torque.
P denoted as the power
\omega denoted as angular velocity or angular speed
So, putting the value and we get,
\tau = \frac{15}{12}
\tau = 1.25 Newton – meter
A boy plays with his toy. When the boy is spinning his toy that time the he applied the power on his toy about 15 Watt. Now the toy starts to spinning at the rate of 12 radians per second.
So, the amount of torque is 1.25 Newton – meter.
Problem statement with solution:-2
A truck is travelled from Kolkata to Mumbai. When the wheel of truck is spinning that time the amount of applied the power on the wheel is about 20 Watt. Now the wheel of the truck starts to spinning at the rate of 15 radians per second.
Now estimate the amount of torque.
Solution:-
Given data are,
Power (P) = 20 Watt.
Angular velocity (\omega) = 15 radians per second
Need to calculate the value of torque (\tau) =?
We know,
The formula for the torque and angular velocity or angular speed is,
Torque = \frac{Power}{Speed}
\tau = \frac{P} {\omega}
Where,
\tau is denoted as Torque.
P denoted as the power
\omega denoted as angular velocity or angular speed
So, putting the value and we get,
\tau = \frac{20}{15}
\tau = 1.33 Newton – meter
A truck is travelled from Kolkata to Mumbai. When the wheel of truck is spinning that time the amount of applied the power on the wheel is about 20 Watt. Now the wheel of the truck starts to spinning at the rate of 15 radians per second.
So, the amount of torque is 1.33 Newton – meter.
Conclusion:
Force around an axle is inversely proportional to speed or angular velocity. Increases value of velocity torque is decrease and decrease value of velocity torque is increase.
Also Read:
- How to determine velocity in pendulum motion
- How to calculate velocity in quantum field theory
- Zero velocity graph
- How to find the kinetic energy and velocity
- Drag coefficient and velocity
- How to find velocity from displacement
- How to measure velocity in spectrometry
- How to find velocity using derivatives
- How to calculate velocity in wormholes
- How to find acceleration with velocity and distance
Hi..I am Indrani Banerjee. I completed my bachelor’s degree in mechanical engineering. I am an enthusiastic person and I am a person who is positive about every aspect of life. I like to read Books and listen to music.