# Calculate Angular Velocity & Force: Mass m, Length 1.25m, Speed 25rpm

• bahramm
In summary, The question involves a rotating mass attached to a point by a string and has two parts. In part (a), the mass is rotating in a horizontal circle and the angular velocity is calculated using the formula w^2=g/h. In part (b), the force on the table is calculated when the speed of rotation is given at 25 rpm and the mass is 6 kg. The solution involves finding the angular velocity, tension, and the vertical and horizontal components of the string.

#### bahramm

Hi guys. I need some help to solve this question.

(a) A body of mass m kg is attached to a point by string of length
1.25 m. If the mass is rotating in a horizontal circle 0.75 m below the
point of attachment, calculate its angular velocity.

(b) If the mass rotates on a table, calculate the force on the table when
the speed of rotation is 25 rpm and the mass is 6 kg.

I got part a) w^2=g/h w=3.61 rad s^-1
part b ?

find the the angular velocity from "the speed of rotation is 25 rpm" if i understand it correctly they gave You the frequency(convert to 1/sec) no problems getting W.
then you can find the H,and the angle the sting is spread.
find the tension(first horizontal component) than find the vertical component, and the rest is easy.
good luck I'm off now.

## 1. What is angular velocity?

Angular velocity is the measure of how quickly an object is rotating around a fixed point. It is usually expressed in radians per second (rad/s) or revolutions per minute (rpm).

## 2. How do you calculate angular velocity?

Angular velocity can be calculated by dividing the change in angle by the change in time. The formula is: angular velocity = change in angle / change in time. It can also be calculated by multiplying the rotational speed (in rpm) by 2π and converting to the desired units.

## 3. How does mass affect angular velocity?

In the given scenario, the mass does not directly affect the angular velocity. However, if the mass is increased while keeping the length and speed constant, the moment of inertia will increase, resulting in a decrease in angular velocity according to the formula: angular velocity = speed / moment of inertia.

## 4. What is the relationship between angular velocity and linear velocity?

Angular velocity and linear velocity are directly proportional to each other. This means that if the angular velocity increases, the linear velocity will also increase, and vice versa. The relationship is described by the formula: linear velocity = angular velocity x radius.

## 5. How can we calculate the force needed to maintain this angular velocity?

The force needed to maintain a constant angular velocity depends on the moment of inertia and the angular acceleration. The formula for calculating force is: force = moment of inertia x angular acceleration. In this scenario, the force can be calculated by first finding the moment of inertia using the formula: moment of inertia = 0.5 x mass x (length)^2, and then using the given angular velocity to calculate the angular acceleration.