Question

A disk of radius 10 cm speeds up from rest. it turns 60 radians reaching an angular velocity of 15 rad/s. what was the angular acceleration?

b. how long did it take the disk to reach this velocity?​

Answer 1

Answer:
`1.875\ rad/s^2, 8\ s`

Step-by-step explanation:

Given

Radius of disc
`r=10\ cm`

Angle turned
`\theta=60\ rad`

Initial angular velocity
`\omega_0=0`

Final angular velocity
`\omega_f=15\ rad/s`

using
`\omega^2-\omega_o^2=2\alpha \cdot \theta`

Substitute values

`\Rightarrow 15^2-0=2* \alpha * 60\\\Rightarrow \alpha=1.875\ rad/s^2`

using
`\omega=\omega_o+\alpha t`

Substitute values

`\Rightarrow 15=0+1.875* t\\\Rightarrow t=8\ s`