# Rotational kinematics of circular saw

• MozAngeles
In summary, the blade of a circular saw slows down from 4740 rpm to 0 in 3 seconds. The angular acceleration of the blade is 9.81 rad/s2.
MozAngeles

## Homework Statement

When a carpenter shuts off his circular saw, the 10.0-inch diameter blade slows from 4740 rpm to zero in 3.00 s.
A. What is the angular acceleration of the blade(rev/s^2)? GOT IT
B. What is the distance traveled by a point on the rim of the blade during the deceleration(ft)? GOT IT
C. What is the magnitude of the net displacement of a point on the rim of the blade during the deceleration(in)? NEED HELP

## Homework Equations

$$\theta$$=s/r
all of the angular kinematics equations

## The Attempt at a Solution

i solved part be with s=$$\theta$$*r after i had found theta using the kinematics equation ($$\omega$$^2=$$\omega$$0^2+2$$\alpha$$*$$\Delta$$$$\theta$$, solving for theta using the acceleration from part A. IF you think part C is just the answer to part B in inches that's wrong, but I do not know what else to do. PLease help.

Imagine a circle. The top of the circle represents the starting point. Where is the end point of its motion? Draw an arrow between those points. That's the displacement.

so the net displacement is the diameter of the wheel, right? So then to i use the S- theta*r, but for r use 10?

MozAngeles said:
so the net displacement is the diameter of the wheel, right?
Only if the net angular displacement is an odd multiple of pi radians. In other words, only if the point of the blade ends up on the opposite side of the circle after it stops.

So then to i use the S- theta*r, but for r use 10?
Not sure what you mean here.

Think about this: How many revolutions does the blade make? If it makes one complete revolution, the net displacement is zero. It's back where it started. If it makes 2.5 revolutions, it is 180 degrees away, thus the displacement equals the diameter. And so on.

Make sense?

I would approach this problem by first defining the variables and equations needed to solve it. In this case, we are dealing with rotational kinematics, so we can use the following equations:

1. \omega = \omega_0 + \alpha t
2. \theta = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2
3. \omega^2 = \omega_0^2 + 2 \alpha \theta

Where:
- \omega is the angular velocity in radians per second
- \omega_0 is the initial angular velocity in radians per second
- \alpha is the angular acceleration in radians per second squared
- t is the time in seconds
- \theta is the angular displacement in radians
- \theta_0 is the initial angular displacement in radians

Now, let's solve for part A. We are given the initial and final angular velocities, as well as the time, so we can use equation 1 to find the angular acceleration:

\alpha = \frac{\omega - \omega_0}{t} = \frac{0 - (4740 \text{ rpm}) \times (2\pi \text{ rad/rpm})}{3.00 \text{ s}} = -318.3 \text{ rad/s}^2

For part B, we need to find the distance traveled by a point on the rim of the blade during the deceleration. Since we know the angular acceleration, we can use equation 2 to find the angular displacement:

\theta = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2 = 0 + (4740 \text{ rpm}) \times (2\pi \text{ rad/rpm}) \times (3.00 \text{ s}) + \frac{1}{2} (-318.3 \text{ rad/s}^2) (3.00 \text{ s})^2 = -3581 \text{ rad}

Now, we can use the relationship \theta = s/r to find the distance traveled by a point on the rim of the blade:

s = \theta r = (-3581 \text{ rad}) \times (10.0 \text{ in}/2) = -17905 \text{ in}

Since distance cannot be negative, we

## What is rotational kinematics of circular saw?

Rotational kinematics of circular saw refers to the study of the motion and behavior of a circular saw blade as it rotates around its axis. This includes analyzing its speed, acceleration, and angular displacement.

## What factors affect the rotational kinematics of a circular saw?

The rotational kinematics of a circular saw can be affected by various factors such as the diameter and material of the saw blade, the power of the saw motor, and the type of material being cut.

## How is rotational kinematics of circular saw different from linear kinematics?

Rotational kinematics deals with the motion of objects around a fixed axis, while linear kinematics deals with the motion of objects in a straight line. Additionally, rotational kinematics involves angular measurements such as radians and degrees, while linear kinematics uses linear measurements such as meters or feet.

## What are some real-life applications of rotational kinematics of circular saw?

Rotational kinematics of circular saw has several practical applications in industries such as carpentry, construction, and metalworking. It is also used in the development and improvement of saw blades and other cutting tools.

## How can rotational kinematics of circular saw be calculated and measured?

The rotational kinematics of a circular saw can be calculated and measured using various equations and tools such as rotational motion sensors, tachometers, and protractors. These measurements can help determine the speed, acceleration, and angular displacement of the saw blade.

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