00:01
This question, a constant force of 40 newton is applied tangentially to the rim of a wheel, which is initially atrest as shown in the figure below.
00:10
So the figure is not, i'll just draw the figure over here.
00:14
So this is the rim of the wheel, and this is how the 40 newton is applied tangentially to it.
00:21
Now, the wheel has a moment of inertia of 30 kilogram meter square that is already given in the question.
00:28
And radius of the circle is already given as 0 .2.
00:31
So this is 0 .2 meters.
00:34
First part, we have to find an angular acceleration.
00:37
Pretty straightforward because torque is nothing but i alpha, right? and what is torque? torque is r cross f.
00:46
R cross f is i alpha.
00:48
Now, since the force is tangentially, so with respect to its distance, because definitely it moves about an axis passing through.
00:58
Its center so it's distance from the center or from the point of the axis is nothing but the radius and the angle is 90 degree because the tangent is perpendicular to the radius so our cross -f means it's rf sine of theta which is equal to i alpha and let's substitute the values now r is 0 .2 force is 40 theta is 90 i is the moment of inertia which is given as 30 and alpha is what we have to find so we're on the left side.
01:30
Let me just get my calculator.
01:33
So it's 0 .2 times 40 times sign 90.
01:37
90 is 1.
01:37
So 8 is equal to 30 alpha.
01:39
And dividing both sides by 30, we have 8 over 30 as alpha.
01:44
So if you flip the equation, the value of alpha is 8 over 30.
01:48
And the value of 8 over 30, 8 over 30 comes out as 0 .27 radian per second square.
01:58
This is this is the required value of alpha all right in part two they're asking that what is the angular velocity after four seconds so that's where the equation of kinematics comes in i mean equation of kinematics which is applied for the you know the angular the rotation part so uh i think we can use omega is equal to omega not plus alpha t omega not is the initial velocity initial angular velocity and since it starts from rest it's given over here so that should that would be zero alpha is the angular acceleration which you just found as 0 .27 from here and time is four seconds as given in the question so all we have to do is multiply our angular acceleration with four which will come out as 1 .07 and the unit is radiant per second all right let's move ahead with the next part so the number of revolution after four seconds so again now we can use the equation uh equation of motions once again so but this time we got to use i think the second equation of motion that theta is equal to omega knot t plus half alpha t squared initial angular velocity is 0 .27 and the time is 4 second so we have 4 square so this value comes out as a 0 .2 seven times 16 over two which is coming as 2 .16 but what is this 2 .16 this 2 .16 is in radiance but what do they need they need the number of revolutions so they're not a problem we can convert the number of revolutions because we know the relationship between the radian and the revolution right we know that 2 pi radiant 2 pi radiant basically means one complete circle that corresponds to one revolution so 2 .1 16 radium will correspond to 1 over 2 pi times 2 .16 revolution...