elgringo

I have been set a question to answer, although i do not know where to start, could anyone help or give me a starting poing please?

A swing bridge of mass 6500 kg has to be turned through an angle of 92 degrees in 148 seconds. The first 52 seconds is a period of uniform angular acceleration, the subsequent 30 seconds is a period of uniform velocity and the third period of uniform angular retardation. Find the maximum angular velocity, the acceleration and retardation. If the radius of gyration of the bridge is 7.794 kgm², determine the torques required to start and stop the bridge moving.

## Answers and Replies

J77
I'd start by drawing a picture and make notes of what's happening at the different stages.

bdrosd
I am assuming that the bridge swings horizontally, and that what you call the radius of gyration is what most call the "moment of inertia". Before going further, some of your numbers look suspicious. If the mass is 6500kg, how can the moment of inertia be only 7.794 kgm^2 ? (seems too small) . As J77 suggests, make a plot of angular velocity versus time and note the three different regions of angular acceleration. Label the value of acceleration in each, and set up an equation that sums the amount of rotation that occurs during each of these three periods. Based on the constraint that a total of 92 degree of rotation must occur in 148 seconds you can solve for the initial angular acceleration. The deceleration in the 3rd period of time can be stated in terms of the initial acceleration. You are going to have to do a fair bit of manipulation of the angular kinematic equations to arrive at a solution for intial acceleration, but it will work. Once you have that, finding torque only requires the use of Newton's 2nd law (for rotations). And finally, dont forget to do all this in radians, not degrees.

elgringo
Its a tough one for me as the college lecturer only seems to hand out notes and never goes through examples with the class. This is making it hard, trying to learn the subject from books and internet pages.

I appreciate the help from you both, more help or suggestions are more than welcome!

Cheers guys

bdrosd
Use the rotational kinematic equations to determine the amount of rotation in each of the three constant acceleration sections of the motion (acc. is zero in the middle one). You will have to come up with values (or expressions) for the initial and final rotational velocities in each case. In certain cases the initial velocity of one section will be the final velocity of the previous one. Once you have these three expressions, sum them since that sum must equal 92 degree (in radians). Good luck