A ball is tied to a string and whirled in a horizontal circle at a constant...

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)

Solutions

Expert Solution

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

genius_generous answered 2 years ago

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