# Angular velocity acceleration

• tahyus
In summary, the conversation discusses a solid sphere with a mass of 1.5 kg and radius of 15 cm moving down a 35 degree incline. The question asks for the angular velocity in rad/s at the bottom of the incline, assuming it starts from rest. The suggested method is to use the principle of conservation of energy, where gravitational potential energy is converted into angular and translational kinetic energy. The relation v=rw can be used to solve for the angular velocity, assuming rolling without slipping occurs. The steps suggested are to find the angular acceleration using the L=I(angular velocity) equation, then use the relation v=rw to solve for the angular velocity.
tahyus
1. a solid sphere (I=0.4mr^2) of mass 1.5 kg and radius 15 cm moves down a 35 degrees incline 7m long. Assuming it started from rest, what is its angular velocity in rad/s at the bottom of the incline? a)71.27 b)32.25 c)49.98 d)61.69

3.i tried by plugging in the values and trying to find the angular acceleration so i could use the L=I(angular velocity) equation; but my numbers just don't add up. pls guide me through the process

thnx

ty

Use the principle of conservation of Energy. The gravitational potential energy is converted into Angular Kinetic Energy.

The gravitational potential energy is converted into angular KE AND translational KE. Assuming that rolling without slipping happens here, you can use the relation v=rw to solve for the angular velocity.

can someone pls provide me with a mathematical representation of the previous replies?

or at least outline the steps that i will need to follow

im a bit confused about all this

thnx

ty

## What is angular velocity acceleration?

Angular velocity acceleration refers to the rate of change of angular velocity, which is the measure of how quickly an object is rotating around a fixed axis. It is a vector quantity, meaning it has both magnitude and direction.

## How is angular velocity acceleration calculated?

Angular velocity acceleration is calculated using the formula a = (v2 - v1) / (t2 - t1), where a is the angular acceleration, v1 and v2 are the initial and final angular velocities, and t1 and t2 are the initial and final times.

## What is the difference between angular velocity and angular acceleration?

Angular velocity is a measure of how quickly an object is rotating, while angular acceleration is a measure of how quickly the angular velocity is changing. In other words, angular velocity is the rate of change of angular displacement, while angular acceleration is the rate of change of angular velocity.

## How is angular velocity acceleration related to linear velocity acceleration?

Angular velocity and linear velocity are related through the equation v = rw, where v is the linear velocity, r is the radius of the circular motion, and w is the angular velocity. Similarly, angular acceleration and linear acceleration are related through a = rw^2, where a is the linear acceleration and w is the angular acceleration.

## What are some real-life examples of angular velocity acceleration?

Some real-life examples of angular velocity acceleration include the spinning of a merry-go-round, the rotation of a Ferris wheel, and the movement of a car's tires while turning. It is also seen in the rotation of planets and other celestial bodies.

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