A disk with mass m = 9.2 kg and radius R = 0.3? m begins at rest and accelerates

Question

A disk with mass m = 9.2 kg and radius R = 0.3? m begins at rest and accelerates uniformly for t = 17.9 s, to a final angular speed of ? = 35 rad/s.
1)What is the angular acceleration of the disk



2)What is the angular displacement over the 17.9 s?


3)What is the moment of inertia of the disk?

4)What is the change in rotational energy of the disk?


5)What is the tangential component of the acceleration of a point on the rim of the disk when the disk has accelerated to half its final angular speed?

6)What is the magnitude of the radial component of the acceleration of a point on the rim of the disk when the disk has accelerated to half its final angular speed?



7)What is the final speed of a point on the disk half-way between the center of the disk and the rim?




8)What is the total distance a point on the rim of the disk travels during the 17.9 seconds?

Explanation / Answer

Mass of the disk m = 9.2 kg Radius of the disk R = 0.3 m Initial angular velocity i = 0 Final angular velocity f = 35 rad/s Time interval t = 17.9 s ---------------------------------------------------- (a) Angular acceleration of the disk                    = (f - i) / t                       = 35 rad/s / 17.9 s                       = 1.955 rad/s2 (b) Angular dispalcement                    = 1/2 t2                       = (0.5) (1.955 rad/s2 )(17.9 s)2                       = 313 rad (c) Moment of inertia of disk                     I = 1/2 MR2                       = (0.5)(9.2 kg) (0.3 m)2                       = 0.414 kg m2 (d) The change in rotational energy of the disk                   K = 1/2 I2                         = (0.5)(0.414 kg m2) (35 rad/s)2                        = 253.575 J (e) Tangential component of acceleration                    at = R                       = (0.3 m) (1.955 rad/s2 )                       = 0.586 m/s2 (f) Radial acceleration                    ar = R2                         = (0.3 m) (35 rad/s /2)2                         = 91.875 m/s2 (g) Final speed v = r = (0.3 /2)(35 rad/s)                                     = 5.25 m/s (h) Total distance                        s = R                           = (0.3 m) (313 rad)                           = 93.9 m (g) Final speed v = r = (0.3 /2)(35 rad/s)                                     = 5.25 m/s (h) Total distance                        s = R                           = (0.3 m) (313 rad)                           = 93.9 m

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