When a carpenter shuts off his circular saw, the 10.0-inch diameter blade slows from 4665 rpm to zero in 2.00 s. What is the distance traveled by a point on the rim of the blade during the deceleration? (in ft). What is the magnitude of the net displacement of a point on the rim of the blade during the deceleration? (in inches)

Question

When a carpenter shuts off his circular saw, the 10.0-inch diameter blade slows from 4665 rpm to zero in 2.00 s. What is the distance traveled by a point on the rim of the blade during the deceleration? (in ft). What is the magnitude of the net displacement of a point on the rim of the blade during the deceleration? (in inches)

Answer 1

To find the distance traveled by a point on the rim of the blade during deceleration, we can use the formula:

distance = (initial velocity + final velocity) * time / 2

Given:
Initial velocity = 4665 rpm
Final velocity = 0 rpm
Time = 2.00 s

We need to convert rpm to inches per second to be consistent with the units of time. One revolution corresponds to the circumference of the blade, which is given by:

circumference = π * diameter

Given diameter = 10.0 inches, the circumference is:

circumference = π * 10.0 inches

To convert rpm to inches per second, we need to divide by 60 since there are 60 seconds in a minute:

velocity = (4665 rpm * circumference) / (60 s)

Substituting the values, we have:

velocity = (4665 rpm * π * 10.0 inches) / (60 s)

Now, we can substitute the values into the distance formula:

distance = ((4665 rpm * π * 10.0 inches) / (60 s) + 0 rpm * π * 10.0 inches) / 2 * 2.00 s

Simplifying the equation:

distance = ((4665 rpm * π * 10.0 inches) / 60 s) / 2 * 2.00 s

distance = (4665 rpm * π * 10.0 inches) / 60 s * 4.00 s

distance = (4665 rpm * π * 10.0 inches * 4.00 s) / 60 s

Now we can calculate the distance traveled by a point on the rim of the blade during deceleration.

To find the magnitude of the net displacement of a point on the rim of the blade during deceleration, we simply need to find the difference between the initial and final positions of the point. Since the final position is zero, the magnitude of the net displacement will be the same as the initial position.

The initial position of a point on the rim of the blade can be calculated using the formula:

initial position = (initial velocity * time) / 60

Substituting the values:

initial position = (4665 rpm * π * 10.0 inches * 2.00 s) / (60 s * 60)

Finally, by converting the initial position from inches to feet, we can find the magnitude of the net displacement.