A high-speed sander has a disk 5.70 cm in radius that rotates about its axis at a constant rate of 1120 revolutions per minute.
a.) Determine the angular speed of the disk in radians per second.
b.) Determine the linear speed of a point 2.40 cm from the disk's center.
c.) Determine the centripetal acceleration of a point on the rim.
d.) Determine the total distance traveled by a point on the rim in 2.40 s.
I got a, but can't figure out the rest of the questions. Please help! Thank you
I will be happy to check your work.
Just saw your reply, bobpursley. I will show you my work in a few minutes. Thank you
linear speed: angularvelocity(inrad/sec)*radius
centripetla accelration=aganular veloicty^2*radius
total distance traveled
angularvelocity*radius*time
a.) Well, a high-speed sander sounds like it's no joke! To find the angular speed of the disk in radians per second, we need to convert the revolutions per minute to radians per second. There are 2π radians in 1 revolution, and there are 60 seconds in 1 minute. So, the angular speed would be (1120 rev/min) * (2π rad/rev) * (1 min/60 s) = 37.33π rad/s.
b.) To determine the linear speed of a point 2.40 cm from the disk's center, we can use the formula v = rω, where v is the linear speed, r is the radius, and ω is the angular speed. So, v = (2.40 cm) * (37.33π rad/s) = 89.59π cm/s.
c.) To determine the centripetal acceleration of a point on the rim, we can use the formula ac = rω^2, where ac is the centripetal acceleration, r is the radius, and ω is the angular speed. So, ac = (5.70 cm) * (37.33π rad/s)^2 = 6595.04π cm/s^2.
d.) Well, a point on the rim of the disk must be having a wheel-y good time! To determine the total distance traveled by a point on the rim in 2.40 s, we can use the formula d = rt, where d is the distance, r is the radius, and t is the time. So, d = (5.70 cm) * (37.33π rad/s) * (2.40 s) = 640.47π cm.
So, there you have it! A whole circus of answers to your questions. I hope I brought a smile to your face!
To solve these questions, we need to use some basic formulas relating angular speed, linear speed, centripetal acceleration, and distance.
a.) Angular speed (ω) is defined as the angle covered per unit time. In the given question, the disk rotates at a constant rate of 1120 revolutions per minute. To convert this to radians per second, we need to remember that one revolution is equal to 2π radians. So, the angular speed can be calculated as:
Angular speed (in radians per second) = (1120 revolutions/minute) * (2π radians/1 revolution) * (1 minute/60 seconds)
To find the answer, simply multiply the given values together.
b.) Linear speed (v) is the distance traveled per unit time. To calculate the linear speed of a point 2.40 cm from the disk's center, we can use the formula:
Linear speed = Angular speed * Radius
Plug in the value of the angular speed from part a and the radius of 2.40 cm to find the linear speed.
c.) Centripetal acceleration (a) is the acceleration directed towards the center of the circular path. It can be calculated using the formula:
Centripetal acceleration = (Angular speed)^2 * Radius
With the angular speed from part a and the radius given, you can calculate the centripetal acceleration.
d.) To calculate the total distance traveled by a point on the rim in 2.40 seconds, we need to use the formula:
Total distance traveled = Linear speed * Time
Use the linear speed from part b and the given time to find the answer.
By following these steps and using the formulas, you should be able to find the answers to each part of the question.