A turntable that spins at a constant 80.0 rpmrpm takes 3.50 ss to reach this angular speed after it is turned on. Find its angular acceleration (in rad/s2rad/s2), assuming it to be constant, and the number of degrees it turns through while speeding up.

The angular acceleration is 2.39 rad/s².

The number of degrees it rotates is 841.68 degrees.

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.

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