Question

A uniform disk is constrained to rotate about an axis passing through its center and perpendicular to the plane of the disk. If the disk starts from rest and is then brought in contact with a spinning rubber wheel, we observe that the disk gradually begins to rotate too. If after 35 s of contact with this spinning rubber wheel, the disk has an angular velocity of 4.0 rad/s, find the average angular acceleration that the disk experiences. (Assume the positive direction is in the initial direction of rotation of the disk. Indicate the direction with the sign of your answer.)

Answer 1

Step-by-step explanation:

Given:

Initial velocity, wi = 0 rad/s

Final velocity, wf = 4 rad/s

Time, t = 35 s

Using equation of motion,

wf = wi + ao × t

Angular acceleration, ao = (4 - 0)/35

= 0.114 rad/s^2

B

Initial velocity, wi = 0 rad/s

Final velocity, wf = 11 rad/s

Time, t = 35 s

Using equation of angular motion,

calculating ao,

ao = 11/35

= 0.3143 rad/s^2

wf^2 = wi^2 + 2ao × θ

Angular distance, θ = (11^2)/(2 × 0.3143)

= 192.5 rad

Answer 2

A uniform disk is constrained to rotate about an axis passing through its center and perpendicular to the plane of the disk. If the disk starts from rest and is then brought in contact with a spinning rubber wheel, we observe that the disk gradually begins to rotate too. If after 35 s of contact with this spinning rubber wheel, the disk has an angular velocity of 4.0 rad/s, find the average angular acceleration that the disk experiences. (Assume the positive direction is in the initial direction of rotation of the disk. Indicate the direction with the sign of your answer.)

Assume after 35 s of contact with this spinning rubber wheel, the disk has an angular velocity of 11.0 rad/s.

Answer:

385 rad

Step-by-step explanation:

The expression for the angular acceleration of a disk that is in contact with a spinning wheel can be given as:

`\alpha = (\delta \omega)/(\delta t)`

where
`\delta\omega` =
`\omega_f - \omega_i`

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

`\alpha = ( 4.0 rad/s-0 rad/s)/(35)`

`\alpha =0.14 rad/s^2`

Angular displacement of a disk can be calculated by using the formula:

`\theta = \omega t`

substituting 11.0 rad/s for
`\omega` and t = 35 s ; we have:

`\theta = 11.0 rad/s * 35 s`

`\theta = 385 rad`