Consider an object undergoing a rotational motion in the xy-plane about a fixed

Question

Consider an object undergoing a rotational motion in the xy-plane about a fixed axis perpendicular to the plan of motion. Let O be a point in the xy-plane along the axis of rotation and P is a fixed point on the object. Due to the rotation of the object, point P will experience a circular motion with the radius of its circular path r = 0.6 m. Assume that at some point in time, the angular acceleration of point P is = 5 rad/s2 and an angle between the vectors of its tangential and net acceleration is = 30% Determine the magnitude of linear velocity (v) of point P and the magnitude of its tangential (at), normal (an) and net (a) acceleration vectors.

Explanation / Answer

According to the concept of the circular motion

Given that

Angular acceleration =5 rad/s^2

Angle =30°

Radius r=0.6 m

Now we find the tangential acceleration

Tangential acceleration At=r=0.6*5=3 m/s^2

Now we find the centripetal acceleration

Centripetal acceleration Ac

Tan30=At/Ac=3/Ac

Ac=3/tan30=5.2 m/s^2

Centripetal acceleration Ac=5.2 m/s^2

Now we find the net acceleration

The net acceleration a=(5.2^2+3^2)^1/2

=6 m/s^2

Now we find The linear velocity

V=(5.2*0.6)^1/2=1.8 m/s

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