A discus thrower (arm length 0.7 m) starts from rest and begins to rotate counte

Question

A discus thrower (arm length 0.7 m) starts from rest and begins to rotate counterclockwise with a constant angular acceleration of +1.5 rad/s2. (a) How many radians of angle does it take for the discus thrower's angular velocity to reach +6.9 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

a. use the kinematic equation Wf^2 - Wi^2 2 A T

A is angular accleraton and T is Theta

so Theta = angular displacement = Wf^2 -Wi^2 /2A

Theta T = 6.9^2 -0^2/(2 * 1.5)

theta = 15.87 radians

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B . usw Wf = Wo + At

t = 6.9 -0/1.5

t = 4.6 secs

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C: use linear speed V = r W

V = 0.7 * 6.9

V = 4.83 m/s

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d. tangential accleration a = LA

a = 0.7 * 1.5

a = 1.05 rad/s^2

Ar = rW^2

Ar = 0.7 * 6.9* 6.9 = 33.32 m/s^2

accleratio a^2 = at^2 + ar^2

a^2 = 33.32^2 + 1.05^2

a = 33.33 m/s^2

tan theta = ac/at = (33.32/1.05)

tan theta = 31.73

theta = 88.19 deg

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