rolling motion

The tangential acceleration of each point on the rim of a rolling object is different from other points as no two points possess the same direction.

Regarding the magnitude of acceleration, if the object rolls withou slipping, the magnitude of the tangential acceleration at each point on the rim equals the the translation acceleration of the centre.

Suppose the object has radius R, and angular velocity w, then the tangent velocity at each point on the rim is given by,
v = Rw
i.e. dv/dt =R(dw/dt)
but dv/dt is the linear acceleration of a point on the rim, i.e. the tangential acceleration
hence, a(tangential) = R(dw/dt) ----------------- (1)

Now, if the objects rolls without slipping, the resultant velocity at the lowest point in contact with the ground is zero, i.e. the tangential velocity equals to the translational velocity of the centre, but in opposite direction. Hence, the translation speed Vt is also given by,

Vt = v = R(w)
which, after differentiation, leads to
d(Vt)/t = R(dw/dt)
Hence. a(translation) = R(dw/dt) ------------------ (2)
When comparing (1) and (2)
we get, a(tangential) = a(translation)

Notice that such relation holds only under the condition that the object rolls without slipping.

那麼物體滾動的加速度的值是否等於其切線加速度的值??

我看不懂你再說什麼

不過一個物體滾動的加速度

不是切線加速度