Solving for Torque and Angular Speed in an Engine

In summary, the problem involves finding the constant torque required to bring an engine wheel with a moment of inertia of 2.80kgm^2 up to an angular speed of 360 rev/min in 7.60 seconds, starting from rest. The equation used is "Torque = I*alpha", which is the rotational version of Newton's 2nd law. The final kinetic energy can be found using the rotational version of the kinetic energy formula, which is K = 0.5*I*omega^2. Mass is not needed for this calculation.
  • #1
Heat
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[SOLVED] Torque & Angular Speed

Homework Statement



The wheel of an engine has a moment of inertia 2.80kgm^2 about its rotation axis.

What constant torque is required to bring it up to an angular speed of 360 rev/min in a time of 7.60 s, starting from rest?

What is its final kinetic energy?

Homework Equations



torque = rF sin(theta)
k=.5mv^2

The Attempt at a Solution



First I converted 360 rev/min to seconds

so

360 (rev/min) ( 1 min/60s)( 2pi/rev) = 37.699 rad/s

t = 7.60

I = 2.80 kgm^2

so I decided to get angular acceleration, in case I need it is

alpha = 4.96

From what I spotted in my book Sum of torque = I(angular acceleration)

torque = (2.80)(4.96)
torque = 13.89

this is right, but is they way I have done it correct or did I just get lucky. I am afraid I just plugged into the "sum of torquez = I (angular accelerationz)"

without understanding it :O

part two of the question is

What is its final kinetic energy?

for this

K=.5mv^2

how do I implement this into the problem if I don't have mass?

omega = omega initial + alpha(time)
 
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  • #2
Heat said:

The Attempt at a Solution



First I converted 360 rev/min to seconds

so

360 (rev/min) ( 1 min/60s)( 2pi/rev) = 37.699 rad/s

t = 7.60

I = 2.80 kgm^2

so I decided to get angular acceleration, in case I need it is

alpha = 4.96

From what I spotted in my book Sum of torque = I(angular acceleration)

torque = (2.80)(4.96)
torque = 13.89

this is right, but is they way I have done it correct or did I just get lucky. I am afraid I just plugged into the "sum of torquez = I (angular accelerationz)"

without understanding it :O
That's fine. Realize that the equation "Torque = I*alpha" is just the rotational version of Newton's 2nd law; the translational version (which you know and love) is "Force = mass*acceleration".

part two of the question is

What is its final kinetic energy?

for this

K=.5mv^2

how do I implement this into the problem if I don't have mass?
You don't need mass. For rotational kinetic energy, use I. What's the rotational version of the kinetic energy formula?

Read this: Rotational-Linear Parallels
 
  • #3
Great! Thank you very much Doc Al, you are the greatest. :)
 

What is torque?

Torque is a measure of the force that can cause an object to rotate around an axis. It is often represented by the symbol "τ" and is measured in units of newton-meters (N·m) in the SI system.

What is angular speed?

Angular speed is a measure of how fast an object is rotating around an axis. It is usually represented by the symbol "ω" and is measured in units of radians per second (rad/s) in the SI system.

What is the relationship between torque and angular speed?

The relationship between torque and angular speed is described by the equation τ = Iω, where τ is torque, I is moment of inertia, and ω is angular speed. This equation states that the torque applied to an object is directly proportional to its moment of inertia and angular speed.

How is torque and angular speed related to rotational motion?

Torque and angular speed are essential concepts in rotational motion. Torque causes a rotational acceleration, and the resulting angular speed determines the rate at which an object rotates around an axis. They are fundamental in understanding and predicting the behavior of rotating objects.

What are some real-life applications of torque and angular speed?

Torque and angular speed have various applications in everyday life, such as in the operation of machines, vehicles, and sports equipment. They are also crucial in understanding the motion of planets and other celestial bodies in space.

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