Question

Simple pendulum, is show in several states In case A the mass is travelling back down to the bottom and is in between the bottom and its max height. In case B the mass is at its max height and has a speed of zero. In case C the ball is at its lowest position which of the following statements about the magnitude of the mass's angular acceleration is true? Grade Sun O
It is maximum in case A O
It is maximum in case B O
It cannot be determined O
It is zero in all cases. O
It is maximum in case C
It is equal in all cases, but is non-zero

Answer 1

The angular acceleration is maximum in case C

Explanation:

The motion of the bob in the simple pendulum is a portion of a circular motion. In a circular motion, the angular acceleration is related to the tangential acceleration by

$a=\alpha r$

where

a is the tangential acceleration

$\alpha$ is the angular acceleration

r is the radius (the length of the pendulum)

Moreover for a pendulum, the tangential acceleration is given by the component of the acceleration of gravity in the tangential direction, so

$a=g sin \theta$

where

g is the acceleration of gravity

$\theta$ is the angle of the pendulum with the vertical

So we have

$\alpha = \frac{g sin \theta}{r}$

Since g and r are constant, we see that the angular acceleration is proportional to the angle: the larger the angle, the larger the angular acceleration, and the smaller the angle, the smaller the angular acceleration.

Therefore, the angular acceleration is maximum when the pendulum is at its maximum height, and zero when it is at the lowest position. So, the correct statements are

It is maximum in case C

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