Question

A ball is tied to a string and whirled in a horizontal circle at a constant 4 revolutions per second. Categorize the following according to whether they are constant and zero in value, constant and non-zero in value, or non-constant in value:

linear speed (scalar)

linear velocity (vector)

radial (centripetal) acceleration (scalar)

radial (centripetal) acceleration (vector)

angular speed (scalar)

angular velocity (vector)

angular acceleration (scalar)

angular acceleration (vector)

Answer 1

Given, Angular velocity of the ball is cnstant.

And, Angular velocity \((\omega)=4\) revolutions per second.

- linear speed (scalar): Constant.

Because, Linear speed \((v)=\omega r\)

Since, \(\omega\) and \(r\) (radius of circular motion) is constant. Thus the linear speed will be constant.

- linear velocity (vector) : Changes (Non-constant).

Because, During the circular motion - the direction of motion changes constantly. Thus linear velocity will changes.

- radial (centripetal) acceleration (scalar): Constant.

Because, it depens on linear speed which is constant, Thus centripetal acceleration will be constant.

- radial (centripetal) acceleration (vector): Changes (Non-constant).

- angular speed (scalar): Constant. (Given)

- angular velocity (vector) : Constant

- angular acceleration (scalar) : Zero

Because, Angular acceleration is rate od chage of anular velocity. Here, Angular velocity is constant. So, Angular acceleration will be Zero.

- angular acceleration (vector) : Zero