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.

Rotational Motion

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.

Rotational Motion Help

(B) Angular velocity:

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

The instantaneous angular velocity rotational motion image4is

rotational motion image5

The direction of rotational motion image4 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 rotational motion image6

The instantaneous angular acceleration, rotational motion image7

rotational motion image8

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


rotational motion image9 … (i)

Þ vT = wr

Where vT is tangential speed.

Differentiating, equation (i) once again

rotational motion image10

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

rotational motion image12

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