A flywheel with a 15-cm diameter is rotating at a rate of 7 radians //sec. What is the linear speed of a point on its rim, in centimeters per minute?

Calculate Radius: To find the linear speed of a point on the rim of the flywheel, we need to use the formula for linear speed (v), which is the product of the radius (r) of the flywheel and the angular speed (ω), given by v = r * ω. First, we need to find the radius of the flywheel by dividing the diameter by 2. Diameter of flywheel = 15 cm Radius (r) = Diameter / 2 Radius (r) = 15 cm / 2 Radius (r) = 7.5 cmCalculate Linear Speed: Now we have the radius, we can calculate the linear speed using the angular speed (ω) given in radians per second. Angular speed (ω) = 7 radians/sec Linear speed (v) = r * ω Linear speed (v) = 7.5 cm * 7 radians/sec Linear speed (v) = 52.5 cm/secConvert to cm/min: The question asks for the linear speed in centimeters per minute, not seconds. To convert from seconds to minutes, we multiply by the number of seconds in a minute, which is 60. Linear speed (v) in cm/min = Linear speed (v) in cm/sec * 60 Linear speed (v) in cm/min = 52.5 cm/sec * 60 Linear speed (v) in cm/min = 3150 cm/min

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A flywheel with a 15-cm diameter is rotating at a rate of 7 radians //sec. What is the linear speed of a point on its rim, in centimeters per minute?

A flywheel with a $15-\mathrm{cm}$ diameter is rotating at a rate of $7$ radians $/ \mathrm{sec}$ . What is the linear speed of a point on its rim, in centimeters per minute?

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Q. A flywheel with a

15-\mathrm{cm}

diameter is rotating at a rate of

7

radians

/ \mathrm{sec}

. What is the linear speed of a point on its rim, in centimeters per minute?

Calculate Radius: To find the linear speed of a point on the rim of the flywheel, we need to use the formula for linear speed $v$ , which is the product of the radius $r$ of the flywheel and the angular speed $\omega$ , given by $v = r \times \omega$ . First, we need to find the radius of the flywheel by dividing the diameter by $2$ . $\newline$ Diameter of flywheel = $15$ cm $\newline$ Radius $r$ = Diameter / $2$ $\newline$ Radius $r$ = $15$ cm / $2$ $\newline$ Radius $r$ = $r$ $2$ cm
Calculate Linear Speed: Now we have the radius, we can calculate the linear speed using the angular speed ( $\omega$ ) given in radians per second. $\newline$ Angular speed ( $\omega$ ) = $7$ radians/sec $\newline$ Linear speed ( $v$ ) = $r \cdot \omega$ $\newline$ Linear speed ( $v$ ) = $7.5$ cm $\cdot 7$ radians/sec $\newline$ Linear speed ( $v$ ) = $52.5$ cm/sec
Convert to cm/min: The question asks for the linear speed in centimeters per minute, not seconds. To convert from seconds to minutes, we multiply by the number of seconds in a minute, which is $60$ . $\newline$ Linear speed ( $v$ ) in cm/min = Linear speed ( $v$ ) in cm/sec $*$ $60$ $\newline$ Linear speed ( $v$ ) in cm/min = $52.5$ cm/sec $*$ $60$ $\newline$ Linear speed ( $v$ ) in cm/min = $v$ $0$ cm/min