Calculating Torque and Work for an Electric Trimmer Blade | Homework Help

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In summary: The ω2 is 66.15, while ω1 is 0. Plugging in the values would give me 3.87x10^-5JIn summary, to find the torque needed to accelerate an electric trimmer blade from rest to 605 RPM in 1.05 seconds, we use the equation Torque=Ixα and convert the RPM to rad/s. The torque required is 9.35x10^-3N-m and the work done to accelerate the blade is 3.87x10^-5J. The correct equations to use are ω=ωi+αt and W=\frac{1}{2}Iω^{2}_{2}-\frac{1}{
  • #1
nickb145
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Homework Statement



An electric trimmer blade has rotational inertia 1.55×10−4kg⋅m2 .

What torque is needed to accelerate this blade from rest to 605rpm in 1.05s ?

How much work was done to accelerate the blade?

Homework Equations



Torque=Ixα
rpm=>Rad/s
α=Δω/Δy

The Attempt at a Solution



Ok so i converted RPM to Rev/s first. which is 63 rad/s now substituting it in for α and multiply it by the Inertia will get me the torque of 9.35x10^-3N-m

Angular Velocity i think is 66.15rad/s. Because ω=α*T
For the work, it is just the change in kinetic energy right? K=(.5)(I)ω^2 i keep getting a wrong answer
 
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  • #2
RPM and rad/s are measures of angular velocity, and angular velocity is not the same as angular acceleration.

You have an initial angular velocity of 0 and a final angular velocity of 605 RPM (converted to rad/s) which is to be achieved in 1.05 s. What angular acceleration (units of rad/s^2) is required to do this? Once you find the ang. acceleration, then you'll be able to calculate the torque required to do this.

You should have studied the basic equations of angular motion (and they are analogous to the equations of linear motion).
 
  • #3
α is angular acceleration. you used the angular velocity, 605rpm (63rad/s) to find the torque. Your KE equation is correct but you used the wrong value for angular velocity. The angular velocity was given.
 
  • #4
SteamKing said:
RPM and rad/s are measures of angular velocity, and angular velocity is not the same as angular acceleration.

You have an initial angular velocity of 0 and a final angular velocity of 605 RPM (converted to rad/s) which is to be achieved in 1.05 s. What angular acceleration (units of rad/s^2) is required to do this? Once you find the ang. acceleration, then you'll be able to calculate the torque required to do this.

You should have studied the basic equations of angular motion (and they are analogous to the equations of linear motion).

Yeaa, i noticed that. Wasn't thinking straight.

I would think that i would use one of my kinematic equations ω=ωi+αt to find α which in this case is just ω=60
(.5)(1.55x10^-4)(60^2)=.279

IS there anything i am forgetting?
 
Last edited:
  • #5
Scratch that, that one is for constant acceleration. This isn't constant
 
  • #7
mishek said:
Isn't the work done equal to the change in rotational kinetic energy:

W=[itex]\frac{1}{2}[/itex]I[itex]ω^{2}_{2}[/itex]-[itex]\frac{1}{2}[/itex]I[itex]ω^{2}_{1}[/itex]

http://hyperphysics.phy-astr.gsu.edu/hbase/rotwe.html

yes that is what i meant
 

What is torque and why is it important in science?

Torque is the measure of the force that causes an object to rotate around an axis. It is important in science because it helps us understand how forces affect the motion of objects and how to control that motion.

How is torque calculated?

Torque is calculated by multiplying the magnitude of the force applied to an object by the perpendicular distance from the axis of rotation to the point where the force is applied. The unit of torque is Newton-meters (Nm) in the SI system.

What factors affect torque?

The magnitude and direction of the force applied, as well as the distance from the axis of rotation to the point where the force is applied, all affect torque. The angle at which the force is applied also plays a role in determining the torque.

How is torque related to angular acceleration?

Torque is directly proportional to the angular acceleration of an object. This means that a larger torque will result in a greater angular acceleration, while a smaller torque will result in a smaller angular acceleration.

What are some real-life applications of torque?

Torque is used in many real-life applications, such as tightening screws, opening doors, and pedaling a bicycle. It is also important in engineering and mechanics, such as in the operation of engines, motors, and machines.

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