(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?

m/s2

(b) When the disk is at its final speed, what is the tangential velocity of the bug?
m/s

(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 will be happy to critique your work.

well, 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.

and for the second one, i took the rad/s and multiplied it times .1524m to get m/s and it said i was incorrect again.

To find the tangential acceleration of the bug on the rim of the disk, we can use the formula:

Tangential acceleration = (Change in angular velocity) / (Time taken)

(a) First, we need to convert the diameter of the disk to meters, since the unit of the final answer is in m/s^2. The diameter of 6.0 inches is equal to 0.1524 meters (1 inch = 0.0254 meters).

Next, we need to convert the angular velocity from revolutions per minute (rev/min) to radians per second (rad/s). To do this, we multiply the angular velocity by 2π/60 (since there are 2π radians in a full revolution and 60 minutes in an hour). The angular velocity of 79 rev/min is equal to (79 * 2π/60) rad/s.

Now we have the necessary values to calculate the tangential acceleration. Plugging these values into the formula:

Tangential acceleration = ((79 * 2π/60) rad/s) / (5.0 s)

Simplifying, we get:

Tangential acceleration = (79 * 2π/60) rad/s^2 / 5.0 s

Evaluating this expression, the tangential acceleration of the bug on the rim of the disk is the final answer for part (a) in m/s^2.

(b) To find the tangential velocity of the bug when the disk is at its final speed, we can use the formula:

Tangential velocity = (Radius of the disk) * (Angular velocity)

The radius of the disk is half of its diameter, so it is equal to 0.1524 meters / 2 = 0.0762 meters.

Plugging in the values:

Tangential velocity = (0.0762 m) * (79 * 2π/60) rad/s

Simplifying and evaluating this expression gives the tangential velocity of the bug in m/s, which is the answer for part (b).

(c) To find the tangential acceleration of the bug one second after it starts from rest, we can use the same formula as in part (a) since it measures the change in angular velocity over a certain time period.

Since the time period is now 1 second, we can calculate the tangential acceleration in the same way as in part (a), but with a different time value of 1 second.

For the centripetal acceleration, we need to use the formula:

Centripetal acceleration = (Tangential velocity)^2 / (Radius of the disk)

We already calculated the tangential velocity in part (b), and we have the radius of the disk as 0.0762 meters. Plugging these values into the formula gives the centripetal acceleration in m/s^2.

For the total acceleration, we need to use the Pythagorean theorem since the total acceleration consists of both tangential acceleration and centripetal acceleration. We can calculate it as:

Total acceleration = sqrt((Tangential acceleration)^2 + (Centripetal acceleration)^2)

Evaluating this expression gives the total acceleration in m/s^2.

For the relative angle between the tangential acceleration and the total acceleration, we can use trigonometry to calculate it. We can calculate the angle between these two vectors using the formula:

Angle = arctan((Centripetal acceleration) / (Tangential acceleration))

Evaluating this expression gives the relative angle in degrees.

By following these steps, you should be able to find the answers to parts (a) to (c) of the given question.