Question

A Wheel has an angular acceleration of 3.0 rad/s² and an initial angular speed of 2.00 rad/s. In a time of 2s it has rotated thorough an angle (in radian) of:

6

10

12

4

Solution

Angular acceleration is time derivative of angular speed and angular speed is time derivative of angular displacement.
By definition,
$straight alpha space equals space dω over dt ie comma space dω space equals space αdt So comma space if space in space time space straight t space the space angular space speed space of space straight a space body space changes space from space straight omega subscript straight o space to space straight omega integral subscript straight omega subscript straight o end subscript superscript straight omega space dω space equals space integral subscript 0 superscript straight r space straight alpha space dt If space straight alpha space is space constant straight omega space minus straight omega subscript straight o space equals space αt straight omega space equals space straight omega subscript straight o space plus αt Now comma space as space by space definition straight omega space equals space dθ over dt Eq space left parenthesis straight i right parenthesis space becomes dθ over dt space equals space space straight omega subscript straight o space plus αt dθ space equals space left parenthesis straight omega subscript straight o space plus αt right parenthesis dt So space straight m space if space in space time space straight t space angular space displacement space is space straight theta integral subscript 0 superscript straight theta dθ space equals space integral subscript 0 superscript straight t space left parenthesis straight omega subscript straight o space plus αt right parenthesis space dt Given comma space straight alpha space equals space 3.0 space rad divided by straight s squared comma space space equals space 2.0 space rad divided by straight s comma space straight t space equals space 2 straight s Hence comma space straight theta space equals space 2 space straight x space 2 space plus space 1 half space straight x space 3 space left parenthesis 2 right parenthesis squared or space straight theta space equals space 4 plus 6 space equals space 10 space rad$

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Units And Measurement

A Wheel has an angular acceleration of 3.0 rad/s² and an initial angular speed of 2.00 rad/s. In a time of 2s it has rotated thorough an angle (in radian) of:

6

10

12

4

Some More Questions From Units and Measurement Chapter

To measure a physical quantity X, the unit U is repeatedly used for n times. What is the magnitude of physical quantity?

Does the numerical factor in the quantitative measurement depend on the system of unit used?

Is one unit sufficient to measure a physical quantity?

Can a physical quantity have two or more units? Give example.

What are fundamental quantities?

How many fundamental quantities are there in mechanics?

How many fundamental quantities are there in Physics?

Name the fundamental quantities of mechanics.

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For Daily Free Study Material Join wiredfaculty

Units And Measurement

A Wheel has an angular acceleration of 3.0 rad/s2 and an initial angular speed of 2.00 rad/s. In a time of 2s it has rotated thorough an angle (in radian) of: 6 10 12 4

Some More Questions From Units and Measurement Chapter

To measure a physical quantity X, the unit U is repeatedly used for n times. What is the magnitude of physical quantity?

Does the numerical factor in the quantitative measurement depend on the system of unit used?

Is one unit sufficient to measure a physical quantity?

Can a physical quantity have two or more units? Give example.

What are fundamental quantities?

How many fundamental quantities are there in mechanics?

How many fundamental quantities are there in Physics?

Name the fundamental quantities of mechanics.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A Wheel has an angular acceleration of 3.0 rad/s² and an initial angular speed of 2.00 rad/s. In a time of 2s it has rotated thorough an angle (in radian) of:

6

10

12

4