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SAMPLE PROBLEMS: 111-SET #9 ROTATIONAL MOTION PROBLEMS: 09-1

1) A grinding wheel starts from rest and has a constant angular acceleration of 5 rad/sec2. At t = 6 seconds find the centripetal and tangential accelerations of a point 75 mm from the axis. Determine the angular speed at 6 seconds, and the angle the wheel has turned through.

|We have a problem of constant angular acceleration. The figure & coordinate system are |[pic] |
|shown. Since a time is given in the problem we must use the equations of motion. | |
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|((t) = (1/2) ( t2 + ( 0 t ; ((t) = ( t + ( 0 | |
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|The initial state of motion is: ( 0 = 0; ( 0 = 0 . We are given ( in the problem. | |
|Hence we have the specific equations of motion: | |

((t) = (1/2)(5) t2 ; ((t) = 5 t .

Thus at time t = 6 sec, ((6 sec) = (5)(6) = 30 rad/sec . And: ((6 sec) = (1/2)(5)(6)2 = 90 rad .

The centripetal & tangential accelerations are linear quantities. Hence, to calculate we need the interconnecting equations. ( s = r (( ; v = r ( ; a t = r (

(Where all angular quantities are expressed in terms of angular units of radians.) Thus, at 6 seconds we have: for velocities