Derive the relation,

$straight theta equals straight theta subscript 0 plus straight omega subscript 0 straight t plus 1 half αt squared$

for uniform angular accelerated motion.

Solution

We know,
Angular velocity, $straight omega equals dθ over dt$
or $dθ equals straight omega space dt$
For uniform angular accelerated motion,
$space space space space space space space space space straight omega space equals space straight omega subscript straight o space plus space αt space therefore space space space dθ space equals space left parenthesis straight omega subscript straight o space plus space αt space right parenthesis space dt space Integrating space both space sides comma space we space get integral subscript straight theta subscript straight o end subscript superscript straight theta dθ space equals space integral subscript 0 superscript straight t left parenthesis straight omega subscript straight o space plus space αt space right parenthesis space dt space equals straight omega subscript straight o space integral subscript 0 superscript straight t dt space plus space straight alpha space integral subscript 0 superscript straight t straight t space dt space rightwards double arrow space space space right enclose straight theta space subscript straight theta subscript straight o end subscript superscript straight theta space equals right enclose space straight omega subscript straight o straight t end enclose subscript 0 superscript straight t space plus space 1 half right enclose αt squared end enclose subscript 0 superscript straight t space rightwards double arrow space space straight theta space minus space straight theta subscript 0 space equals ωt space plus space 1 half αt squared rightwards double arrow space straight theta space equals space space straight theta subscript 0 space plus ωt space plus space 1 half αt squared$
Hence, proved.

Some More Questions From Laws of Motion Chapter

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Laws Of Motion

Derive the relation,

$straight theta equals straight theta subscript 0 plus straight omega subscript 0 straight t plus 1 half αt squared$

for uniform angular accelerated motion.

Some More Questions From Laws of Motion Chapter

Define inertia.

When the branches of an apple tree are shaken, the apples fall down. Why?

A person jumping out from a moving car or bus falls forward. Why?

Due to what type of inertia, the spark leaves the grind stone tangentially while sharpening the knife?

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?

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