a high speed sander has a disk of 2.74 cm in radius that rotates its disks about the axis at a constant rate of 503 rev/min. determine the linear speed of a point 2.33 cm from the disk's center. answer in units of m/s
tangential speed=radius*w
w=503rev/min(1min/60sec)(2PIrad/rev) to get into rad/sec
put radius into meters.
To determine the linear speed of a point on the disk, we need to find the circumference of the disk first. The formula for the circumference of a circle is:
C = 2πr
where C is the circumference and r is the radius of the circle.
In this case, the radius of the disk is given as 2.74 cm. So, substituting the value into the formula:
C = 2π * 2.74 cm
Now, we need to convert the circumference from centimeters to meters since the answer is required in m/s. There are 100 centimeters in 1 meter. Therefore:
C = (2π * 2.74) / 100 m
Next, we need to find the linear speed of a point 2.33 cm from the disk's center. To find the linear speed, we multiply the rotational speed (in revolutions per minute) by the circumference (in meters) at that distance from the center.
First, we need to convert the rotational speed from rev/min to rev/s. There are 60 seconds in 1 minute, so we divide 503 by 60:
Rotational speed = 503 rev/min / 60 s/min
Now, we multiply the rotational speed by the circumference at the given distance from the disk's center:
Linear speed = Rotational speed * Circumference
Linear speed = (503 rev/min / 60 s/min) * (2π * 2.33 cm) / 100 m
Calculating the value:
Linear speed = (503 / 60) * (2 * 3.14 * 2.33 / 100) m/s
Therefore, the linear speed of a point 2.33 cm from the disk's center is approximately equal to the calculated value in m/s.