Physics Help Forum angular acceleration

 Mar 15th 2019, 02:24 AM #1 Junior Member   Join Date: Feb 2019 Posts: 2 angular acceleration Hi I need some help with this: The grinding disc of a grinding machine starts from a rest and has a constant angular acceleration for the first 10 rotations. a) It uses 0.87 s on its second rotation. how long does it use on the first rotation? Her i found out that it use 0.62s on the first rotation! b) What is the angular acceleration of the disc for the 10 rotations. give the answer in radians / s ^ 2? is this the right formula to use? ∝=(ω_1-ω_0)/(t_1-t_0 ) Do i need to find out the time it use on the 10 rotasion?
 Mar 15th 2019, 11:21 AM #2 Senior Member   Join Date: Aug 2010 Posts: 389 Let the constant, a, be the constant angular acceleration in rotations per seconds. Then starting from rest, the angular velocity after t seconds is at and the actual rotation is (a/2)t^2. One rotation will be completed after (a/2)t^2= 1 so t= sqrt(2/a). Two rotations will be completed in (a/2)t^2= 2 so t= sqrt(4/a). The time used on the second rotation is sqrt(4/a)- sqrt(2/a)= (2- sqrt(2))/sqrt(a)= 0.87. So sqrt(a)= (2- sqrt(2))/0.87= 0.586/0.87= 0.67 rotations per second per second. As above the time taken for one rotation sqrt(2/a)= sqrt(2/0.67)= 1.73 seconds. topsquark and star89 like this.
 Mar 15th 2019, 11:35 AM #3 Senior Member     Join Date: Jun 2016 Location: England Posts: 750 This can perhaps be approached more as a maths problem. The acceleration is linear: standard equation for a linear function is y=mx+c for this case it starts from rest so c=0 replace m with the rate of acceleration (a), x with time (t) and y with rotation rate (w) so w=at but you want to know the rotation position, so you need to integrate the rate. p = 1/2at^2 (note p is in radians; I will use "pi" to represent 3.14...) Now it gets a little but awkward, you are given the time between p=2pi and p=4pi (i.e. the time between the end of the first rotation and the end of the second rotation) so 4pi-2pi = 1/2at2^2 - 1/2at1^2 does this give you enough to carry on from? (HallsOfIvy types faster than I do) topsquark and star89 like this. __________________ ~\o/~
 Mar 16th 2019, 02:40 AM #4 Junior Member   Join Date: Feb 2019 Posts: 2 aaah okey Thank you so much for the help

 Tags acceleration, angular

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