A discus thrower (arm length 1.2 m) starts from rest and begins to rotate counte

Question

A discus thrower (arm length 1.2 m) starts from rest and begins to rotate counterclockwise with a constant angular acceleration of +3.0 rad/s2.
(a) How many radians of angle does it take for the discus thrower's angular velocity to reach +6.0 rad/s?
?rads
(b) How long does this take?
? seconds

At this time (from part b), please find the following quantities:

(c) the linear speed of the discus:
? m/s

(d) the size of the discus's tangential acceleration:
? m/s2
the size of the discus's centripetal acceleration:
? m/s2

the size of the discus's total acceleration:
? m/s2
the angle that the total acceleration makes with the velocity vector is:
? degrees

Explanation / Answer

Given The radius of the rotatory motion is , r = 1.2 m Angular acceleration, = 3.0 rad/s^2 Final angular velocity , = 6.0 rad/s a) From the relation   ^2 - i^2 = 2                                  (6.0rad/s)^2 - 0 = 2 ( 3.0 rad/s^2)                                    = 6 rad b) Time taken is calculated from the relation                   = i t + 1/2 t^2                6 rad = 0 + 0.5( 3.0 rad/s^2) t^2                      t = 2 s c) Linear speed , v = r                               = 1.2m (6 rad/s) = 7.2 m/s d) Tangential acceleration, at = r = 1.2m ( 3.0 rad/s^2)                                             = 3.6 m/s^2 Centripetal acceleration, ac = v^2 / r = (7.2 m/s)^2 / 1.2 m                                           = 43.2 m/s^2 Total acceleration, a = ( at )^2 + (ac )^2                                  = (3.6m/s^2)^2 + (43.2 m/s^2)^2                              a = 43.35 m/s^2 Angle made by the total acceleration makes with velocity vector is cos = 7.2 / 43.35        = 80.40

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