Angular acceleration homework problem

In summary: So, can you summarize the content for me?In summary, a bug on the rim of a 8.0 in. diameter disk experiences a tangential acceleration of .1596 m/sec^2 as the disk moves from rest to an angular speed of 75 revolutions per minute in 5.0 s. The tangential velocity of the bug at the disk's final speed is .79796 m/s. One second after starting from rest, the bug experiences the same tangential acceleration of .1596 m/sec^2. To find the centripetal acceleration, the equation a = v²/r is used, with a radius of .1016 m and a tangential velocity of .79796 m/s. The total acceleration
  • #1
Dr_bug
17
0

Homework Statement


What is the tangential acceleration of a bug on the rim of a 8.0 in. diameter disk if the disk moves from rest to an angular speed of 75 revolutions per minute in 5.0 s?
(b) When the disk is at its final speed, what is the tangential velocity of the bug?

(c) One second after the bug starts from rest, what is its tangential acceleration?

What is its centripetal acceleration?

What is its total acceleration (magnitude and angle relative to the tangential acceleration) ?

Homework Equations


atan= R*angular acceleration
v= R*w
ac=R*w^2

The Attempt at a Solution


I was able to answer a, b, and the first part of c but I can't get the centripetal acceleration . For (a) I got .1596 m/sec^2 (b) .79796 m/ sec (c) the atan after 1 sec is the same as (a). To find the ac I used the third equation but didn't get the right answer... is that the right equation to use to find centripetal acceleration? I converted 4 in into .1016 m and used that for R and then multiplied it by 7.85 rad/sec^s... i could use some help
 
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  • #2
I don't agree with your (a) and (b) answers . . . can you show the calcs?
Once you have the v value from (b) it should be easy to find a = v²/r.
 
  • #3
sure (a):
(4 in* 2.54 cm*75 rev*2pi rad)/(100 cm*60 sec*5 sec)= .1596 m/sec^2 -- I know its right because I already submitted it online and it accepted the answer.
(b):
(4 in* 2.54 cm*75 rev*2pi rad)/(100 cm*60 sec)= .79796 m/s -- this was also accepted
 
  • #4
Oh, I didn't notice the inches! Agree.
 
  • #5
so should I then take .79796 and square it and then divide by .1016 (thats the radius converted to meters)
 
  • #6
Right!
 

FAQ: Angular acceleration homework problem

1. What is angular acceleration and how is it different from linear acceleration?

Angular acceleration is a measure of the rate of change of angular velocity of an object. It is different from linear acceleration because it measures the change in the object's rotational speed, rather than its linear speed.

2. How is angular acceleration calculated?

Angular acceleration is calculated by dividing the change in angular velocity by the change in time. The formula for angular acceleration is: α = (ω2 - ω1) / (t2 - t1), where α is the angular acceleration, ω2 and ω1 are the final and initial angular velocities, and t2 and t1 are the final and initial times.

3. What are the units of angular acceleration?

The units of angular acceleration are radians per second squared (rad/s²) in the SI (International System of Units) system. In other systems, it can also be expressed as degrees per second squared (deg/s²) or revolutions per second squared (rev/s²).

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

Angular acceleration affects an object's rotational motion by changing its angular velocity. If the angular acceleration is positive, the object will speed up its rotation, while a negative angular acceleration will cause the object to slow down its rotation. A zero angular acceleration means the object's rotational speed remains constant.

5. Can you provide an example of an angular acceleration homework problem?

Sure, an example of an angular acceleration homework problem could be: A disc starts rotating at an initial angular velocity of 10 rad/s and accelerates at a rate of 2 rad/s² for 5 seconds. What is the final angular velocity of the disc? The solution would be: α = (ω2 - ω1) / (t2 - t1) → 2 = (ω2 - 10) / (5-0) → ω2 = 20 rad/s.

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