Question

A rotating platform of radius R starts from rest and accelerates with uniform angular acceleration α.

a. Write a symbolic expression for the time at which the magnitudes of the centripetal and tangential accelerations at the edge will be equal.

b. Now let R=2.4 cm=2.4 cm and α=44 rad/s=44 rad/s. Calculate the time, t in seconds, for when the magnitudes of the centripetal and tangential accelerations are equal.

Answer 1

The time at which the magnitudes of the centripetal and tangential accelerations at the edge of a rotating platform are equal is 1 second. For a platform with a radius of 2.4 cm and an angular acceleration of 44 rad/s², the time is approximately 0.023 seconds.

Step-by-step explanation:

To find the time at which the magnitudes of the centripetal and tangential accelerations at the edge of a rotating platform are equal, we can equate the formulas for these accelerations. The centripetal acceleration is given by ac = R * α , where R is the radius of the platform and α is the angular acceleration. The tangential acceleration is given by at = R * α * t, where t is the time. Setting ac equal to at, we can solve for t:

R * α = R * α * t

t = 1

Therefore, the time at which the magnitudes of the centripetal and tangential accelerations are equal is 1 second.

For part (b), with R = 2.4 cm and α = 44 rad/s², we can plug these values into the equation we derived in part (a) to find t:

2.4 cm * 44 rad/s² = 2.4 cm * 44 rad/s² * t

Simplifying, we get:

t = 1 / 44 ≈ 0.0227 seconds

Therefore, the time at which the magnitudes of the centripetal and tangential accelerations are equal is approximately 0.023 seconds.