Question

A disk, initially rotating at 120 rpm, is slowed down with a constant acceleration of magnitude 4 rad s2. If the disk has diameter of 20 cm. Determine the time does the disk take to stop i. ii the angle does the disk rotate during that time iii. the total angular distance rotated by a disk

Answer 1

Step-by-step explanation:

given,

ω₁ = 120 rpm

1 rpm =
`(2\pi )/(60) rad/s`

`\omega_1 =120* (2\pi )/(60)` rad/s

= 12.56 rad/s

α = - 4 rad/s²

diameter of disk = 20 cm

final angular velocity = 0

t =
`(\omega_f-\omega_i)/(\alpha)`

t =
`(0-(12.56))/(-4)`

t = 3.14 s.

2)
`\theta = \omega_i t +(1)/(2) \alpha t^2`

=
`12.56* 3.14 +(1)/(2)* (-4)* 3.14^2`

= 19. 72 radians

3) total angular distance rotated

x = θ R

x = 19.72 × 0.1 = 1.97 m

x = 2 m