This question was previously asked in

MPSC AMVI Official Paper 3: 2002

Option 4 : tangential component of acceleration of B relative to A by length AB

MPSC AMVI Official Paper 1: Set A/2017

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150 Questions
300 Marks
90 Mins

**Explanation:**

Acceleration diagram for a link:

The acceleration of any point in a mechanism can be determined by two important methods

- Analytical method
- Graphical or acceleration diagram method

If an expression for displacement in terms of time (t) is known, then the analytical method can be applied.

But for most of the mechanism, the expression for displacement can not be determined easily.

Hence the graphical or acceleration diagram method is generally used.

**Acceleration diagram method**

Fig (a) shows a rigid link AB. Let the point B is moving with respect to point A. To find the acceleration of B relative A, assume point A to be fixed. If A is assumed fixed then the only possible motion of B will be rotation about A as the center.

For a particular instant, ω = Angular velocity of link AB, α = angular acceleration of link AB.

As point B is rotating about A, The velocity of B is changing in magnitude and direction.

Hence the acceleration of point B will have two components

**Radial component**or centripetal component which is due to the angular velocity. It will be acting along BA and will be directed B to A. The magnitude of this component will be v^{2}/r or ω^{2}× r. Hence radial component of B with respect to A.**The tangential component**is due to angular acceleration (α). This acts parallel to the velocity or it is perpendicular to AB. The tangential component of B with respect to A is given by,

**f ^{t}_{BA} = α × BA **

**Hence angular acceleration of the link AB is the ratio of tangential acceleration and length of the link AB.**