Answer:
The angular acceleration is <u>2.39 rad/s²</u>.
The number of degrees it rotates is <u>841.68 degrees</u>.
Explanation:
Given:
Initial angular speed (ω₀) = 0 rad/s
Final angular speed in rpm (N) = 80.0 rpm
Time taken (t) = 3.50 s
First, let us determine the final angular speed in radians per second.
We know that,
Plug in the values and find the final angular speed, 'ω'. This gives,
Now, using equation of motion for rotational motion, we have:
Plug in the given values and solve for α. This gives,
Therefore, the angular acceleration is 2.39 rad/s².
Now, again using rotational equation of motion relating angular displacement, we have:
Plug in the given values and solve for 'θ'. This gives,
Convert radians to degrees using the conversion factor. This gives,
π radians = 180°
So, 1 radian =( 180 ÷ π ) degrees
Therefore,
So, the number of degrees it rotates is 841.68 degrees.