Question

A turntable of 0.8 m in diameter is spinning about its axis with an initial angular velocity of 4 rad/s. If it experiences a constant angular acceleration of 3 rad/s 2 , find: A) The angle through which the turntable has travelled from 0 sec to 2 sec. B) The arc length the turntable’s rim has travelled from 0 sec to 2 sec. C) The tangential speed of the turntable’s rim at t=2 sec. D) The tangential acceleration of the turntable’s rim at t=2sec. E) The radial acceleration of the turntable’s rim at t=2sec

Answer 1

GIVEN  

d = 0.8m

= 4rad/s

= 3rad/s^2

t = 0sec to 2 sec

1)angular velocity =/t

     4 = / 2

so angle = 8 degrees

2) arc length = RC--------(2)

C - central angle of the arc in radians = 8degrees

R - radius of the arc = 0.4m

substituting the values in eqn(2) we have

arc length l = (0.4)(8)(2)/ 360

so l = 0.05m

3) tangential speed

v = r

= (0.4)(4)

v = 1.6m/s

4) tangential acceleration

a = r

= (0.4)(3)

a = 1.2m/s^2

5)radial acceleration

f = i + t

    = (4) + (3)(2)

so f = 10rad/s