Question

In: Physics

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)

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

A ball is attached to a string and swung in a horizontal circle at a constant...

A ball is attached to a string and swung in a horizontal circle at a constant speed. Assume air resistance is negligible. If the string tripled in length but the speed of the ball remained the same, show mathematically how the inward force on the ball would change.

A ball of mass m is tied to a string and is rotating in a vertical...

A ball of mass m is tied to a string and is rotating in a vertical plane. The string is elastic (it stretches), which causes the path to be elongated vertically rather than perfectly circular. At the top of the path, the speed has the minimum value that still allows the ball to complete its circular path. Find: the length of the string when it makes an angle θ with respect to the horizontal. The following quantities are known: Mass...

A massless string is tied to a heavy ball whirling in a vertical plane. 1) At...

A massless string is tied to a heavy ball whirling in a vertical plane. 1) At what angle is the tension in the string a minimum? a) 0o, b) 45o, c) 90o, d) 180o, or e) 270o 2) At what angle is the tension in the string a maximum? a) 0o, b) 45o, c) 90o, d) 180o, or e) 270o 3) The tension is independent of the length of the string. 4) At what angle is the string most likely...

A 1-kg ball is tied to the end of a 2-meter string and revolved in a...

A 1-kg ball is tied to the end of a 2-meter string and revolved in a horizontal plane making a 30o angle with the vertical. (a) What is the ball's speed? (b) If the ball is now revolved so that its speed is 4m/s, what angle does the string need to make with the vertical? (c) If the string can withstand a maximum tension of 10 N, what is the highest speed at which the ball can travel?

An athlete swings a ball, connected to the end of a chain, in a horizontal circle....

An athlete swings a ball, connected to the end of a chain, in a horizontal circle. The athlete is able to rotate the ball at the rate of 8rev/s when the length of the chain is 0.600m. when he increases the length to 0.900 m, he is able to rotate the ball 6.00 rev/s. (a) which rate of rotation gives the greater speed for the ball? (b) what is the centripetal acceleration of the ball at 8.00 rev/s? (c) what...

1. A ball hanging from the ceiling by a string swings in a circle. If the...

1. A ball hanging from the ceiling by a string swings in a circle. If the radius of the circle it traces is 2 meters and its distance from the ceiling is 5 meters, what is the velocity of the ball? 2. Assuming an iced over road (no friction), if a car is going 25 m/s around a curve in the road of radius 75 meters, what is the perfect angle to bank the road so that the car stays...

A 90g ball is tied to a string so that the center its mass hangs 50...

A 90g ball is tied to a string so that the center its mass hangs 50 cm below the point where the string is tied to a support rod. The ball is pulled aside to a60° angle with vertical and released. As the string approaches vertical, it encounters a peg at a distance x below the support rod. The string then bends around the peg. If the position of the peg is low enough, the ball will move in a...

A small 0.11 kg metal ball is tied to a very light (essentially massless) string that...

A small 0.11 kg metal ball is tied to a very light (essentially massless) string that is 0.9 m long. The string is attached to the ceiling so as to form a pendulum. The pendulum is set into motion by releasing it from rest at an angle of 60 ∘ with the vertical. A) What is the speed of the ball when it reaches the bottom of the arc? B)What is the centripetal acceleration of the ball at this point?...

A 3.9 kg ball swings from a string in a vertical circle such that it has...

A 3.9 kg ball swings from a string in a vertical circle such that it has constant mechanical energy. Ignore any friction from the air or in the string. What is the difference in the tension between the lowest and highest points on the circle? Give a positive answer in N.

A 0.25kg ball moving in a horizontal cirlce at the end of a string has a...

A 0.25kg ball moving in a horizontal cirlce at the end of a string has a centripetal acceleration of 4m/s^2. What is the magnitude of the centripetal force exerted by the string on the ball to produce this acceleration?