The first thing we are going to do is find the equation of motion:
ωf = ωi + αt
θ = ωi*t + 1/2αt^2
Where:
ωf = final angular velocity
ωi = initial angular velocity
α = Angular acceleration
θ = Revolutions.
t = time.
We have then:
ωf = (7200) * ((2 * pi) / 60) = 753.60 rad / s
ωi = 0
α = 190 rad / s2
Clearing t:
753.60 = 0 + 190*t
t = 753.60 / 190
t = 3.97 s
Then, replacing the time:
θ1 = 0 + (1/2) * (190) * (3.97) ^ 2
θ1 = 1494.51 rad
For (10-3.97) s:
θ2 = ωf * t
θ2 = (753.60 rad / s) * (10-3.97) s
θ2 = 4544,208 rad
Number of final revolutions:
θ1 + θ2 = (1494.51 rad + 4544.208 rad) * (180 / π)
θ1 + θ2 = 961.57 rev
Answer:
the disk has made 961.57 rev 10.0 s after it starts up
Answer:
% here x and y is given which we can take as
x = 2:2:10;
y = 2:2:10;
% creating a matrix of the points
point_matrix = [x;y];
% center point of rotation which is 2,2 here
x_center_pt = x(2);
y_center_pt = y(2);
% creating a matrix of the center point
center_matrix = repmat([x_center_pt; y_center_pt], 1, length(x));
% rotation matrix with rotation degree which is 45 degree
rot_degree = pi/4;
Rotate_matrix = [cos(rot_degree) -sin(rot_degree); sin(rot_degree) cos(rot_degree)];
% shifting points for the center of rotation to be at the origin
new_matrix = point_matrix - center_matrix;
% appling rotation
new_matrix1 = Rotate_matrix*new_matrix;
Explanation:
We start the program by taking vector of the point given to us and create a matrix by adding a scaler to each units with repmat at te center point which is (2,2). Then we find the rotation matrix by taking the roatational degree which is 45 given to us. After that we shift the points to the origin and then apply rotation ans store it in a new matrix called new_matrix1.
