Consider a pendulum that consists of a ball at the end of a string. The pendulum

Question

Consider a pendulum that consists of a ball at the end of a string. The pendulum executes the motion indicated in the figure below. That is, the pendulum swings back and forth between positions 1 and 3. Where, if anywhere, in the motion is the angular speed of the ball zero? Where in the motion is the angular speed of the ball maximum? Where, if anywhere, in the motion is the tangential acceleration of the ball zero? Where in the motion is the size of the tangential acceleration of the ball maximum? Where, if anywhere, in the motion is the radial acceleration of the ball zero? Where in the motion is the size of the radial acceleration of the ball maximum?

Explanation / Answer

Here ,
as the angular speed is zero at the extreme points

A) the angular speed is zero at 1 and 3

B) at the lowest point , angular speed is maximum

angular speed is maximum at 2

C)

the tangential acceleration is zero at the equilibrium

at the position 2 , tangential acceleration is zero

D)

at the extreme , the tangential acceleration is maximum

the tangential acceleration is maximum at 1 and 3

E)

at the extreme , as the velocity is zero

the radial acceleration is zero at 1 and 3

F)

at the lowest point , as the angular speed is maximum

radial acceleration is maximum at 2

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