Calculate Torque Needed to Spin an LP Turntable 648 Degrees

[mikefitz]

An LP turntable must spin at 3.51 rad/s to play a record. How much torque must the motor deliver if the turntable is to reach its final angular speed in 1.8 revolutions, starting from rest? The turntable is a uniform disk of diameter 31 cm and mass 0.26 kg.

I know that 1.8rev is equal to 648 degrees. This means that the disc must spin 648 degrees to reach the required 3.51 rad/s for the record.

But I don't know how to begin to calculate the torque required to achieve that angular velocity. Where do I begin> Thanks

 

[OlderDan]

An LP turntable must spin at 3.51 rad/s to play a record. How much torque must the motor deliver if the turntable is to reach its final angular speed in 1.8 revolutions, starting from rest? The turntable is a uniform disk of diameter 31 cm and mass 0.26 kg.

I know that 1.8rev is equal to 648 degrees. This means that the disc must spin 648 degrees to reach the required 3.51 rad/s for the record.

But I don't know how to begin to calculate the torque required to achieve that angular velocity. Where do I begin> Thanks

Begin by expressing everything in radians rather than degrees, and by reviewing the equations of rotational kinematics. They are directly analogous to liner kinematics.

 

[mikefitz]

so, total rotation (1.8 rev) is equal to 11.3097 rad. It must spin at 3.51 rad/s.

How do I use this information to calculate a torque? thanks again

 

[OlderDan]

so, total rotation (1.8 rev) is equal to 11.3097 rad. It must spin at 3.51 rad/s.

How do I use this information to calculate a torque? thanks again

Look at your rotational kinematics equations. Find one that relates a change in angular velocity to an angular displacement and a constant angular acceleration. Find another one that relates torque to angular acceleration.

There are other paths to the solution (ther usually are) but these two equations will be a fairly direct route.

 

[mikefitz]

equations my teacher has given me:

KErot = .5 I w^2
I = .5 m r^2
Torque = F r sin(theta)

I guess I am unsure which equation relates all these different elements together?

 

[OlderDan]

equations my teacher has given me:

KErot = .5 I w^2
I = .5 m r^2
Torque = F r sin(theta)

I guess I am unsure which equation relates all these different elements together?

Look here and scroll down to the table showing the linear equations and their angular analogs.

http://online.cctt.org/physicslab/content/PhyAPC/lessonnotes/rotationalmotion/kinematics.asp

You should have seen all of these before. If you have not ssen them, you are seeing them now. Give particular attention to the last one. There is also a rotational analog of Newton's second law

F=ma <> Torque = I*alpha

See what you can do with these.

 

[mikefitz]

great, thanks for the help OlderDan - no I had not seen that last equation until I clicked your link.