2. A flywheel (disk) initially spinning at 1850 rpm...

2. A flywheel (disk) initially spinning at 1850 rpm counterclockwise is brought to rest in 3.00 minutes. a. What is the wheel's average angular acceleration? b. What is the angular displacement of the flywheel during this acceleration? c. If the flywheel has a mass of 155 kg and a radius of 0.650 m, what torque was required to accelerate it? 3. A heavy flywheel rotating counterclockwise about its middle at an original speed of 157.1 rad/s is slowing down because of friction in its bearings. a. If its acceleration is constant at 1.785 rad/s², find its angular velocity at the end of 1.00 minute. b. The flywheel is 5.50 m in diameter and has a mass of 985 kg. If the flywheel resembles a uniform disk, find the torque applied by friction. 4. A uniform solid sphere has a mass of 1.765 kg and a radius of 0.854 m. a. Find the torque required to bring the sphere from rest to an angular velocity of 317 rad/s, clockwise, in 15.5 s. b. What magnitude force applied tangentially at the equator would provide the needed torque?

Transcript

00:01 Okay, so we've got three questions here.

00:03 I'll try and go as quickly as i can without losing anything.

00:06 So number two, we have a disc initially spinning at 1850 rotations per minute counterclockwise.

00:15 It's brought to rest in three minutes.

00:17 And we want to know what the average angular acceleration is, the angular displacement, and then if given the mass and radius, what is going to be the torque that was required to provide that acceleration? so first thing i'm going to do just because it doesn't specify is i'm going to put both of these values in the standard unit, so radiance per second, and then seconds.

00:40 So you have two pi radians in one rotation or revolution, and then one minute over 60 seconds.

00:53 And i do that in my calculator.

01:02 That's going to give me 194 rads per second when i round it and then for three minutes that'll just be 60 seconds over one minute, so that'll be 100 seconds.

01:18 Okay, and then question a is we want to know average acceleration.

01:23 So for that, we'll just use one of the angular kinematic equations that tells us how the angular velocity evolves in time.

01:34 And we'll set this up, so we'll subtract.

01:40 Well, i guess i'm going to plug in values, actually, because i think it'll make the problem a little bit easier if i do that now.

01:45 So we'll have 0 equals 194 plus alpha times 180.

01:52 Then we'll subtract 194.

01:59 So we'll have negative 194 is equal to alpha times 180 and then we'll divide 180 seconds.

02:13 And that's going to give me negative 1 .08 radiance per second squared is our alpha.

02:25 Part b is asking what our change in angle is.

02:30 So i'll use the angular kinematics equation that tells us how angular displacement changes in time.

02:39 So omega -0 -t plus 1 -half alpha t squared.

02:42 Now that we have that alpha, so that'll be, what is that 194, times 180 plus 1 -half negative 1 .08.

02:56 Times 180 squared and that gives me 17 ,484 radians.

03:23 And then our last question is that given the mass is 1555 kilograms, and the radius is 0 .6505 .0 .6 .0.

03:38 Meters, what is the torque? so we can write that the torque is equal to the moment of inertia times alpha, and then the moment of inertia for a disk is one -half mr squared.

03:54 So i'm just going to set that in for i, and then we can put in our 155, and then it asks for, it doesn't specify magnitude so i'm going to keep the negative sign on the alpha so one half 155 .65 squared times 1 .08 gives me 35 and that's going to be newton's oh not each newtons um shoot i can't remember the unit for torque i'm pretty sure it's newton's times meters.

04:43 Yeah, yeah.

04:45 Definitely is.

04:46 Okay, so that's question two.

04:48 Question three, i'll move on to a new page.

04:51 We also have another flywheel.

04:54 It's also rotating counterclockwise.

04:57 We have an original speed in radiance per second this time, so 157 .1 radiance per second, and it's slowing down because of friction.

05:10 So if our angular acceleration is 1 .75 rat per second squared, and we want to include a negative sign since we know it's going to be slowing this thing down.

05:26 We want to know the angular velocity after one minute.

05:29 So what is omega? t equals one minute for 60 seconds.

05:36 We want that to be in seconds.

05:38 So we'll use the same equation we used for part a in the first.

05:41 Previous problem omega plus omega 0 equals alpha t so one 157 .1 minus 1 .785 times 60 one plug that in to my calculator and i get 50 on the dot okay so we've got 50 radians per second...

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