A rotating wheel requires 7.00 s to rotate 25.0 revolutions. Its angular velocit

Question

A rotating wheel requires 7.00 s to rotate 25.0 revolutions. Its angular velocity at the end of the 7.00-s interval is 96.0 rad/s. What is the constant angular acceleration (in rad/s) of the wheel? A rotating wheel requires 7.00 s to rotate 25.0 revolutions. Its angular velocity at the end of the 7.00-s interval is 96.0 rad/s. What is the constant angular acceleration (in rad/s) of the wheel? A rotating wheel requires 7.00 s to rotate 25.0 revolutions. Its angular velocity at the end of the 7.00-s interval is 96.0 rad/s. What is the constant angular acceleration (in rad/s) of the wheel?

Explanation / Answer

let initial angular speed be w1.

final angular speed is 96 rad/sec

if angular acceleration is a,

then final angular speed=initial angular speed+angular acceleration*time

==>96=w1+7*a

==>w1=96-7*a..(1)

angle covered=initial angular speed*time+0.5*angular acceleration*time^2

==>25*2*pi=w1*7+0.5*a*49

==>50*pi=(96-7*a)*7+24.5*a

==>a*(24.5-49)=50*pi-96*7

==>a=21.0172 rad/s^2

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