[請益] 動力學-加速度問題

題目:直徑2m,由靜止開始以順時針方向施以3 rad/sec^2 等角加速度3秒鐘,
試求(a)t=0 (b)t=3 (c)t=5秒,輪子底端之速度及加速度。
(a)
v = w*r
v = v0 + a*t
w = w0 + a*t
w = 0 + 3*0 = 0
v = 0
an = (w^2)*r = 0*1 = 0
at = a*r = 3*1 = 3 m/sec^2
(b)
w = 0 + 3*3 = 9 rad/sec
v = w*r = 9 m/sec
an = (w^2)*r = (9^2)*1 = 81 m/sec^2
at = a*r = 3*1 = 3 m/sec^2
(c)
w = 0 + 3*3 = 9 rad/sec
v = w*r = 9 m/sec
an =(w^2)*r = (9^2)*1 = 81 m/sec^2
at = a*r = 0 * 1 = 0
------------------------------------------------------------------------------
w = 角速度
a = 角加速度
v = 速度
an = 法線加速度
at = 切線加速度
------------------------------------------------------------------------------
小弟的問題,為什麼超過3秒後 w5 = w3呢?
為什麼超過3秒後,計算切線加速度時,a角加速度為零呢?
麻煩版上前輩們不吝嗇指導,謝謝!
試求(a)t=0 (b)t=3 (c)t=5秒,輪子底端之速度及加速度。
(a)
v = w*r
v = v0 + a*t
w = w0 + a*t
w = 0 + 3*0 = 0
v = 0
an = (w^2)*r = 0*1 = 0
at = a*r = 3*1 = 3 m/sec^2
(b)
w = 0 + 3*3 = 9 rad/sec
v = w*r = 9 m/sec
an = (w^2)*r = (9^2)*1 = 81 m/sec^2
at = a*r = 3*1 = 3 m/sec^2
(c)
w = 0 + 3*3 = 9 rad/sec
v = w*r = 9 m/sec
an =(w^2)*r = (9^2)*1 = 81 m/sec^2
at = a*r = 0 * 1 = 0
------------------------------------------------------------------------------
w = 角速度
a = 角加速度
v = 速度
an = 法線加速度
at = 切線加速度
------------------------------------------------------------------------------
小弟的問題,為什麼超過3秒後 w5 = w3呢?
為什麼超過3秒後,計算切線加速度時,a角加速度為零呢?
麻煩版上前輩們不吝嗇指導,謝謝!