A computer disk with a radius of 5 cm starts from rest and speeds up with an ang

Question

A computer disk with a radius of 5 cm starts from rest and speeds up with an angular acceleration of 190rad/s^2 until it reaches its operating speed of 760 rad/s.

a) how many revolutions has it made ten seconds after it starts up?
b) what is the centripital acceleration of a point on the rim of the disk 3 seconds after it is turned on?
c) what is the tangential acceleration of a point on the rim of the disk 3 seconds after it is turned on?
d) what is the centripiteal accelerstion of a point on the rim of the disk 7 seconds after it is turned on?
e) what is the tangential acceleration of a point on the rim of the disk 7 seconds after it is turned on?

Explanation / Answer

Radius = 5cm

= 190 units

Final constant velocity = 760 rad/s

=> Time consumed to attain 760 rad/s = 760/190 = 4 secs

Hence Angle covered in 4 seconds = 1/2 * * 16 = 8 * 190 = 1520 radians

Hence angle covered in next 6 seconds = 760 * 6 = 4560 radians

Total angle covered in 10 seconds = 6080 rad

=> Number of revs = 6080/2 = 967.66 revs

at t=3 = 570 rad/s

=> Cent. acc = ^2 * r = 9747 m/s^2

Tangential acceleration = r = 190 * 3/100 = 5.7 m/s^2

At t=7, = 760

=> Cent. acc = ^2 * r = 17328 m/s^2

t =7 sec , = 0

=> Tangential acceleration = r = 0

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