Question

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s2 turns through 2.4 revolutions during a 2.0-s time interval. What is the angular velocity at the end of this time interval

Answer 1

The angular velocity of the wheel at the end of the time interval is 4.0 rad/s.

Step-by-step explanation:

The angular velocity of a wheel rotating about a fixed axis can be calculated using the equation:

ω = ω0 + αt

Where:

• ω is the final angular velocity
• ω0 is the initial angular velocity
• α is the angular acceleration
• t is the time interval

Given that the wheel starts from rest (ω0 = 0), the angular acceleration is 2.0 rad/s^2, and the time interval is 2.0 s, we can substitute these values into the equation to calculate the final angular velocity:

ω = 0 + (2.0 rad/s^2)(2.0 s) = 4.0 rad/s

Answer 2

Step-by-step explanation:

from equation of motion

`s = ut + (1)/(2)at^2`

`2.4*2\pi = u*2+(1)/(2)*2*4`

u = 5.53 rad/sec

we know that from equation of motion , angular velocity is obtained as

v =u +at

v =5.53 + 2*2

v = 9.536 rad/sec