(a) What is the tangential acceleration of a bug on the rim of a 6.0 in. diameter disk if the disk moves from rest to an angular speed of 79 rev/min 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?
° (relative to the tangential acceleration)
I don't understand how to go from the rad/s to meters/s and all of that.
for the first one, I changed the rev/s to rad/s which was 8.275 rad/s and then i divided that by 5s to get the angular acceleration and then mulitiplied it by the radius (.1524m) in order to change it to tangential acceleration but it said my answer was incorrect.
also, i just looked at it and i believe the answer gives me the wrong units anyways, so I think that is where I am messing up.
I get an angular velocity after 5.0 seconds of 8.273 rad/s. The angular acceleration is 1.655 rad/s. The three inch radius is 0.0762 meters. I believe yu confused the diameter with the radius.
The tangential velocity after 5 seconds is the radius times 8.273 rad/s
To solve this problem, let's break it down into smaller steps and calculate each value one by one.
(a) Tangential acceleration:
1. The angular speed of the disk needs to be converted from revolutions per minute (rev/min) to radians per second (rad/s). To do this, you need to multiply by the conversion factor: 1 rev = 2π rad. So, 79 rev/min is equal to 79 * 2π rad/min.
2. Convert the units from minutes to seconds by dividing by 60: 79 * 2π rad/min / 60. This gives you the angular speed in radians per second.
3. Now, divide the angular speed by the time of 5.0 seconds to find the angular acceleration (α).
4. Multiply the angular acceleration by the radius of the disk (which is half the diameter) to get the tangential acceleration (a).
So, the calculation should be:
τ = (79 rev/min * 2π rad/rev) / 60 s/min
α = τ / 5.0 s
a = α * r, where r is the radius of the disk.
Please note that your method of calculation is almost correct. However, you used the diameter instead of the radius, which caused the incorrect units and the incorrect final answer.
(b) Tangential velocity of the bug:
Once the disk reaches its final angular speed, the tangential velocity of the bug on the rim will be equal to the radius multiplied by the final angular speed of the disk. So, it can be found by multiplying the radius by the final angular speed (ω).
v = r * ω, where v is the tangential velocity.
(c) One second after the bug starts from rest:
One second after the bug starts from rest, its tangential acceleration will still be the same as in part (a). To calculate it, you can use the same method as in part (a).
Centripetal acceleration:
The centripetal acceleration is given by the formula:
ac = ω^2 * r, where ac is the centripetal acceleration and ω is the angular speed.
Total acceleration:
The total acceleration is the vector sum of the tangential acceleration and the centripetal acceleration. To find the total acceleration, use the Pythagorean theorem:
atotal = √(a^2 + ac^2)
Note that the angle (relative to the tangential acceleration) can be found using trigonometry:
θ = arctan(ac / a)
By following these steps, you should be able to calculate all the values correctly.