Derive the relation $straight omega squared minus straight omega subscript straight o superscript 2 equals 2 straight alpha left parenthesis straight theta minus straight theta subscript straight o right parenthesis$ for uniform angular accelerated motion.

Solution

We know,
Angular acceleration,
$space space straight alpha equals dω over dt equals dω over dθ dθ over dt equals dω over dθ straight omega$
$rightwards double arrow space straight omega space dω space equals space straight alpha space dθ$
Now, on integrating both sides, we get
$space space space space space space integral subscript straight omega subscript 0 end subscript superscript straight omega omega space d omega space equals space integral subscript theta subscript o end subscript superscript theta alpha space d theta rightwards double arrow space 1 half right enclose omega to the power of 2 space end exponent end enclose subscript omega subscript 0 end subscript superscript omega space equals space alpha space right enclose theta subscript theta subscript o end subscript superscript theta space rightwards double arrow space 1 half left parenthesis omega squared space minus space omega subscript o squared right parenthesis space equals space alpha space left parenthesis theta space minus space theta subscript o right parenthesis rightwards double arrow space space space space space omega squared space minus space omega subscript o squared space equals space 2 space alpha space left parenthesis theta space minus space theta subscript o right parenthesis$

Some More Questions From Laws of Motion Chapter

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Laws Of Motion

Derive the relation $straight omega squared minus straight omega subscript straight o superscript 2 equals 2 straight alpha left parenthesis straight theta minus straight theta subscript straight o right parenthesis$ for uniform angular accelerated motion.

Some More Questions From Laws of Motion Chapter

Which law of motion is also called law of inertia?

What is measure of inertia of body?

Which law of motion defines the force?

What happens to a stone tied to the end of string and whirled in a circle if the string suddenly breaks?

Which law of motion gives the quantitative knowledge of force?

Which law of motion is the real law of motion?

Which law of motion gives the quantitative definition of force?

Why do we pull the rope in downward direction for climbing up?

What can set the body at rest into motion?

What do you mean by mechanically isolated system?

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