Question

A fan acquires rotation rate of 420 cycle /min with uniform angular acceleration in 11 sec starting from rest . Find -
1- angular acceleration
2- angular displacement during this time interval.​

Answer 1

Explanation:

angular is a right answee

Answer 2

Given: A fan acquires rotation rate of 420 cycle/min with uniform angular acceleration in 11 seconds starting from rest.

To find: Uniform angular acceleration and angular displacement during this time period

Explanation: The rate of rotation is 420 cycle/min or (420/60) cycles/s= 7 cycles/s

We need to convert this to angular frequency to use the dynamics formulas. The formula to convert frequency to angular frequency is:

Angular frequency= 2 * π* frequency

= 2* π * 7

= 14π

Here, Initial angular velocity= 0( starts from rest)

Final angular velocity= 14π and time= 11 s

Let angular acceleration be a.

Formula is: Final ω= Initial ω+ a* time

=> 14 π = 0+ a* 11

=> a = 14π / 11

=> a = 14*3.14 /11

=> a = 3.996 rad/s^2

Let displacement be S.

Formula is: S= initial ω* t + 1/2*a* t^2

= 0+ 1/2* 3.996* 121

= 241.75 rad

Therefore, the angular acceleration in the time interval is is 3.996 rad/ s^2 and angular displacement is 241.75 radians.