Physics Homework Help With Rotational Motion

Rotational Motion

Consider a rigid body rotation about a fixed axis. A body is said to be rigid, if distance between any two particles remain same OR in other words, it can not be deformed.

As the given body is in pure rotational motion every point on it are moving in a circular motion about fixed axis having different radii. Consider two point P and Q located on a body, moving in a circle of radii r1 and r2 respectively. Now, the angle (q) they have turned will be same, but the distances along arc are unequal as their radii are different.

Equations defining the rotation of a rigid body about a fixed axis

The following physical quantities are used to describe a rotational motion.

(A) Angular displacement:

It is defined as the change in angular position (from 1 to 2) of the position vector with respect to any reference line.

Hence the angular displacement Dq is given by Dq = q2 - q1

If angular displacement is large, it is scalar. If it is very small, then it is treated as vectors.

(B) Angular velocity:

The average angular velocity of the body in the time interval t (t2 – t1) is given by

The instantaneous angular velocity is

The direction of is always be perpendicular to the plane containing rotation.

(C) Angular Acceleration:

The average angular acceleration of the rotating body in the interval. (t2 – t1) ,

is given by

The instantaneous angular acceleration,

From figure we have S = qrs ® arc length traveled by the particle

Differentiating,

… (i)

Þ vT = wr

Where vT is tangential speed.

Differentiating, equation (i) once again

rotational motion image11

Þ aT = ar … (ii)

as the point P is moving in a circular path a centripetal acceleration is associated with a which is given as

aC = w2r = vT2 / r … (iii)

The resultant acceleration of quantity is

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