Question

A disc rotates about its axis at speed 25 revolutions per minute and takes 15 s to stop.
Calculate the

i) angular acceleration of the disc.

ii) number of rotation of the disc makes before it stops.

Answer 1

Given ,

n = 25 rpm

n = $\frac{25}{60}$

n = $\frac{5}{12}$ rps

initial angular speed $\omega_o$ = $\frac{5}{12}$ rps

Final angular speed $\omega$ = 0 rad/s

$\omega\ =\frac{5}{12}\ \cdot2\pi$ rad/s

$\omega\ =\ \frac{5}{6}$ rad/s

Time , t = 15s

From kinematics ,

$\omega\ =\omega_o+\alpha t$

$0 =\ \frac{5}{6}\ +\ \alpha\ \left(15\right)$

$\alpha\ =-\frac{1}{18}$

where ,$\alpha$ is angular accelaration.

(ii) number of rotations the disc makes before it stops

in 1 second  disc makes 5/12 rotations

in 15 seconds it makes  $15\cdot\frac{5}{12}$ rotations = $\frac{25}{4}$ rotations

Answer 2

Given: Speed of disc = 25 revolutions per minute

           time taken to stop = 15 second

To find: (i) Angular acceleration of the disc

             (ii) Number of rotation of the discs makes before it stops

Solution:

(i) Initial angular velocity = 25 revolution per minute = 25/60 revolution per                                                          second

                                     = 25/60 rad/sec

Final angular velocity = 0

Time = 15 second

From kinetics,

ω = ω₀ +αt ( where ω₀ is the initial angular speed, ω is the final angular velocity, α is the angular acceleration and t is the time )

o = 10/12 + α×15

α = - 1/18 rad/sec²

(ii) Number of rotation made by disc before it stops

In one second disc makes 25/60 rotations.

Therefore, in 15 seconds disc makes 25/60 × 15 rotations = 25/4 rotations.

Therefore, the angular acceleration of the disc is 25/60 rad/sec,

number of rotations of the disc before it stops is 25/4.