If a wheel of diameter $28$ inches moves at a speed of $100$ kilometers per hour, how many radians per second does it revolve?

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Answer 1 · 2018-02-13T08:35:47

$78.12$ radians per second

As diameter is $28$ , circumference of the wheel is $28pi$ inches or

$28pixx2.54=71.12pi$ cm.

As it travels $100xx1000xx100$ cm. in an hour,

wheel is taking $(100xx1000xx100)/(71.12pi)$ revolutions in an hour or in $3600$ seconds

i.e. $(100xx1000xx100)/(71.12pixx3600)$ revolutions per second

or $(100xx1000xx100)/(71.12pixx3600)xx2pi$ radians per second

i.e. $(100xx1000xx100)/(71.12xx1800)~=78.12$ radians per second

If a wheel of diameter 2828 inches moves at a speed of 100100 kilometers per hour, how many radians per second does it revolve?