A wheel mounted on a stationary axle starts from rest and accelerates with angular acceleration tarannm = 2 + 0.4t rad/s 2 . Find the angular velocity of wheel after 4 seconds of its start. - Wired Faculty

Laws Of Motion

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A wheel mounted on a stationary axle starts from rest and accelerates with angular acceleration tarannm = 2 + 0.4t rad/s². Find the angular velocity of wheel after 4 seconds of its start.

Solution

The angular acceleration of the wheel depends on time.
Therefore, equation of kinematics of uniform accelerated motion is not applicable.
We have here,

straight alpha space equals space 0 space plus space 0.4 space straight t space rad divided by straight s squared space therefore space dω over dt space equals space 2 space plus space 0.4 space straight t space rightwards double arrow space dω space equals space left parenthesis 2 space plus space 0.4 space straight t right parenthesis space dt space On space integrating space both space sides comma space integral subscript 0 superscript straight omega dω space equals space integral subscript 0 superscript 4 left parenthesis 2 space plus space 0.4 space straight t right parenthesis space dt space rightwards double arrow space straight omega vertical line subscript 0 superscript straight omega space equals space left parenthesis 2 straight t space plus space 0.2 space straight t squared right parenthesis vertical line subscript 0 superscript 4 space rightwards double arrow space straight omega space equals space 11.2 space rad divided by sec

This is the required angular velocity of the wheel after t = 4 seconds.

Some More Questions From Laws of Motion Chapter

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Laws Of Motion

A wheel mounted on a stationary axle starts from rest and accelerates with angular acceleration tarannm = 2 + 0.4t rad/s². Find the angular velocity of wheel after 4 seconds of its start.

Some More Questions From Laws of Motion Chapter

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?

Which law of motion gives the quantitative definition of force?

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Laws Of Motion

A wheel mounted on a stationary axle starts from rest and accelerates with angular acceleration tarannm = 2 + 0.4t rad/s2. Find the angular velocity of wheel after 4 seconds of its start.

Some More Questions From Laws of Motion Chapter

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?

Which law of motion gives the quantitative definition of force?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A wheel mounted on a stationary axle starts from rest and accelerates with angular acceleration tarannm = 2 + 0.4t rad/s². Find the angular velocity of wheel after 4 seconds of its start.