Question

What is the average force exerted by the brake?

Answer 1

*** I solved most just need help with two parts

A turntable is set rotating with an angular velocity of 30 rad/s. The turntable has a mass of 2 kg and a radius of 20 cm. (Assume the turntable rotates on its axis with no friction and can be modeled as a disk).

A) What is the rotational inertia of the turntable?
SOLVED: .0004 kg/m
B) What is the angular momentum of the turntable?
SOLVED: 1.2
C) A small lump of clay with a mass of 0.5 kg is dropped on the turntable and sticks to it at a distance of 10 cm from the acis of rotation. (assume the clay can be modeled as a point mass) What is the angular velocity afterwards?
SOLVED: 26.67 rad/sec
D) A rubber pad is then pressed against the outer tim of the disk as a brake and the disk/clay combintation comes to a stop in 8 sec. What is the angular acceleration?
SOLVED: 3.33 rad/sec
E) What is the average force exerted by the break?

F) How much energy was dissipated by the break?

Answer 2

@Data_LG2 @imqwerty

Answer 3

the dissipated energy is the rotational kinetic energy, namely:
\[\Large KE = \frac{1}{2}I{\omega ^2}\]

Answer 4

whereas the average force \(R\), is given by the subsequent formula:
\[\Large R\Delta t = I\omega \]
where \(\Delta t=8\)

Answer 5

R(8)=1.2
r= .15
?

Answer 6

\(I\) is the moment of inertia, and \(\omega\) is the angular speed, so we have:
\[\Large R = \frac{{I\omega }}{{\Delta t}}\]

Answer 7

R = (1.2)/8
R=.15

Answer 8

Iw is 1.2, and T is 8?

Answer 9

we have this:
\[\Large I = m\frac{{{r^2}}}{2} = 2 \cdot \frac{{{{\left( {2 \cdot {{10}^{ - 1}}} \right)}^2}}}{2} = 4 \cdot {10^{ - 2}}\;{\text{Kg \times }}{{\text{m}}^{\text{2}}}\]

Answer 10

Now, if:
\[\Large \omega = 30\;{\text{Hz}}\]
then we have:
\[\Large R = \frac{{4 \cdot {{10}^{ - 2}} \cdot 30}}{8} = ...{\text{newtons}}\]

Answer 11

Yup! this equaties to .15

Answer 12

yes! That's right!