Pendulum and roating disc (circular motion)

[bmchenry]

A pendulum hanging from the edge of a horizontal disk rotating around an axis at a constant rate. The angle that the rotating pendulum makes with the vertical increases with the speed of rotation and can be used as an indicator of speed, calculate speed of disck if R = 0.2m, l = 0.3m and the angle is 42 degrees
R is radius of disc, l is length of rod holding pendulum

When I solved for the velocity of the disk using v2 = g r tanθ where r =R +lsin(theta)

the nswer was incorrect and it asked me if I solved for the velocity of the bob and not the disk, Which I guess I did beciase I got 1.88m/s. The answer in the book for the problem with the same numbers except theta is 45 was 0.89m/s.
I assume if the angle is smaller in my problem the speed would be less than 0.89, is this correct?
Can anyone explain what I did wrong?

Sorry I do not know how to get the diagram into the question

 

[member 553083]

. Yes, you are correct. Since the angle is smaller in your problem, the speed of the disk should be less than 0.89 m/s. The equation you used to solve for the velocity of the disk is incorrect. You need to use the equation v = sqrt(gr tanθ) where r is the distance from the axis of rotation to the pendulum bob. In this case, the distance from the axis of rotation to the pendulum bob is (R + l sinθ). Therefore, you should use the equation v = sqrt(g (R + l sinθ) tanθ). Plugging in the given values, you should get a velocity of 0.75 m/s.