# Motion with constant angular acceleration

• Zoubayr
In summary, the question is asking about the number of revolutions the blade will make when it reaches full speed. To solve this, we can use the angular equations which are analogous to their linear counterparts. To calculate the distance traveled, we use integration twice. The time during which the acceleration happened can be divided into 12 tenths of one second, and the number of full turns completed by the blade within each tenth can be calculated.
Zoubayr
Homework Statement
The blade of a circular saw of diameter 20 cm accelerates uniformly from rest to 7000 rev/min in 1.2 s. What is the angular acceleration? How many revolutions will the blade have made
by the time it reaches full speed?
Relevant Equations
w=2πf
w=w_o +at

Last edited by a moderator:

Zoubayr said:
I am not understanding the 2nd part of the question where it is asked about how many revolutions will the blade make when it reaches full speed.
The angular equations (position, velocity, acceleration) are analogous to their linear counterparts. For linear motion, what mathematical operation do you use (twice) to go from acceleration to distance traveled?

integration

berkeman
Zoubayr said:
...
Let's divide the time during which the acceleration happened into 12 tenths of one second.
How many times the blade completed a full turn within the 0 to 0.1 second?
...
...
How many times the blade completed a full turn within the 1.1 to 1.2 second?

## 1. What is constant angular acceleration?

Constant angular acceleration refers to the rate at which an object's angular velocity changes over time. It is a measure of how quickly an object's rotational speed increases or decreases.

## 2. How is angular acceleration different from linear acceleration?

Angular acceleration is a measure of how quickly an object's rotational speed changes, while linear acceleration is a measure of how quickly an object's linear velocity changes. They are different because rotational and linear motion involve different types of movement.

## 3. What is the formula for calculating angular acceleration?

The formula for calculating angular acceleration is α = (ωf - ωi) / t, where α is the angular acceleration, ωf is the final angular velocity, ωi is the initial angular velocity, and t is the time interval.

## 4. How does angular acceleration affect an object's motion?

Angular acceleration affects an object's motion by changing its angular velocity. If the angular acceleration is positive, the object's rotational speed will increase, and if it is negative, the rotational speed will decrease. This change in rotational speed can also affect the object's linear motion.

## 5. What are some real-life examples of motion with constant angular acceleration?

Some real-life examples of motion with constant angular acceleration include a spinning top, a car accelerating around a curved track, and a roller coaster going through a loop. In all of these cases, the objects are experiencing a change in rotational speed, resulting in a constant angular acceleration.

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