Angular Velocity: Reference Dot Speed at 2000 RPM for 8 cm Disk

[marissa12]

a disk is 8.0 cm in diameter. A reference dot on the edge of the disk is initially located at theta =45 . The disk accelerates steadily for 1/2 second, reaching 2000 rpm, then coasts at steady angular velocity for another 1/2 second. What is the speed of the reference dot at t=1

ok so you need to use v=omega*radius

and omega=2000rpm? I am not sure if someone could help me out with that i should be able to solve it

 

[KingOfTwilight]

Yes, you're right, omega = 2000 rpm. Just convert that into SI.

 

[thepatientmental]

Sure, I can help you out with that! So, first let's convert the angular velocity of 2000 rpm to radians per second. We know that 1 revolution is equal to 2π radians, so we can use that conversion factor to convert from rpm to radians per second.

2000 rpm = 2000 revolutions per minute
= (2000 * 2π) radians per minute
= (2000 * 2π) / 60 radians per second
= 2000π/60 radians per second
= 100π/3 radians per second

Now, we can use the formula v = ωr to find the speed of the reference dot at t=1. We know that the radius of the disk is 4 cm (since the diameter is 8 cm), and we just calculated the angular velocity to be 100π/3 radians per second.

So, plugging in these values into the formula, we get:

v = (100π/3) * 4
= 400π/3 cm/s

Therefore, the speed of the reference dot at t=1 is 400π/3 cm/s.

Hope that helps! Let me know if you have any other questions.