The shaft of the wheel unit rolls without slipping on the fixed horizontal surface. If the velocity and acceleration of point O are 6 ft/sec to the right and 7 ft/sec2 to the left, respectively, determine the accelerations of points A and D.

the acceleration of point A:

the acceleration at point D

Explanation:

To determine the angular velocity ; we use the expression;

where :

= velocity of the wheel

r = radius of the shaft

Replacing 6 ft/s with  and 2 in for r; we have:

Calculating the angular acceleration by using the following expression.

Replacing 7 ft/s² for & 2 in for r

 =

= 42 rad/s

The acceleration at point A can be calculated by using derived equation:

where;

= distance of point A with respect to O

Substituting 7 ft/s² for ; 42 rad/s² for ; 36 rad/s for and 10 for ; we have:

Hence, the acceleration of point A:

To calculate position of D about O ;we have

=

= 0.816 i - 0.1667 j

To determine acceleration of D ; we use the following equation

replacing 7 ft/s² for ; 42 rad/s² for ; 36 rad/s for and  0.816 i - 0.1667 j for ; we have:

Therefore, the acceleration at point D