Physic tangential and Angular Acceleration

[Ravin]

Homework Statement

In a Beams ultracentrifuge, a 20.3 cm long rotor is suspended magnetically in a vacuum. Since there is no mechanical connection to the rotor, the only friction is the air resistance due to the few air molecules in the vacuum. If the rotor is spinning with an angular speed of 4.9 105 rad/s and the driving force is turned off, its spinning slows down at an angular rate of 0.39 rad/s2.

(a) For a point at the end of the rotor, find the initial speed.
105 m/s
(b) For a point at the end of the rotor, find the tangential acceleration component.
m/s2
(c) For a point at the end of the rotor, find the maximum radial acceleration component.
m/s2
I could not figure out a and c please help

Homework Equations

The Attempt at a Solution

 

[cristo]

How did you calculate (a)?

What equations do you know involving acceleration?

 

[baba89]

To find the initial speed, we can use the equation v = ωr, where v is the tangential speed, ω is the angular speed, and r is the radius of the rotor. Plugging in the given values, we get:

v = (4.9 x 10^5 rad/s)(0.203 m)
v = 9.947 x 10^4 m/s

Therefore, the initial speed of a point at the end of the rotor is approximately 9.947 x 10^4 m/s.

To find the tangential acceleration component, we can use the formula a = αr, where a is the tangential acceleration, α is the angular acceleration, and r is the radius of the rotor. Plugging in the given values, we get:

a = (0.39 rad/s^2)(0.203 m)
a = 0.07917 m/s^2

Therefore, the tangential acceleration component for a point at the end of the rotor is approximately 0.07917 m/s^2.

To find the maximum radial acceleration component, we can use the formula ar = ω^2r, where ar is the radial acceleration, ω is the angular speed, and r is the radius of the rotor. Plugging in the given values, we get:

ar = (4.9 x 10^5 rad/s)^2(0.203 m)
ar = 4.705 x 10^10 m/s^2

Therefore, the maximum radial acceleration component for a point at the end of the rotor is approximately 4.705 x 10^10 m/s^2. This is a very large acceleration, which is expected due to the high angular speed of the rotor and the small radius.