First slide

Dynamics of rotational motion about fixed axis

Question

Each of the three balls has a mass m and is welded to the rigid equiangular form of negligible mass. The assembly rests on a smooth horizontal surface. A force F is suddenly applied to one bar as shown in fig. (1). Which of the following statement is connect

Moderate

A

The acceleration of point O is $a = \frac{F}{2 m} i$
B

The acceleration of point O is $a= \frac{F}{m} i$
C

The magnitude of angular acceleration of the frame $α = Fb / ({mr}^{2})$
D

The magnitude of angular acceleration of the frame $α = Fb / (3 {mr}^{2})$

Solution

The net force on the frame = total mass x acceleration
$∴ F = (\begin{array}{ll} 3 m \end{array}) a$
or $a= (\frac{F}{3 m}) \hat{i}$
We know that $τ = Iα = (3 {mr}^{2}) α$
or $Fb = (3 {mr}^{2}) α$
$α = Fb / (3 {mr}^{2})$

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