For a machine with 35-cm -diameter wheels, what rotational frequency (in rpm) do the wheels need to pitch a 85 mph fastball?

Physics

1 answer:

Sav [3.1K]2 months ago

6 0

Answer:

The required rotational frequency is 2073.56 rpm

Explanation:

It's essential to calculate the rotational frequency in "rpm" (revolutions per minute), so we should first convert the input data into suitable units:

The speed for the pitch is specified in miles per hour, while the diameter of the vehicle's wheels is stated in centimeters. We'll convert all lengths to meters (utilizing the metric system) along with time into minutes.

Conversion of 85 mph speed into meters per minute:

Remember that 1 mile is equivalent to 1609.34 meters, and 1 hour is 60 minutes, thus we write:

$85\,\frac{miles}{hour} = 85\,\frac{1609.34\,m}{60\,min} =2279.898\,\frac{m}{min}$

which can be approximated to around 2280 m/min.

The 35 cm diameter is converted to meters as follows:

diameter = 0.35 m

Next, we apply the equation connecting angular velocity (w) and the radius (R) of circular motion to find the wheel's angular velocity:[ $v_t$ ], where the angular velocity is represented in

radians

per unit of time. Therefore, we first determine the radius of the wheel (half the diameter). R = 0.175 m $v_t=w*R\\w=\frac{v_t}{R}$

Now we have:

Remembering that

radians correspond to one revolution, we convert the angular velocity to revolutions per minute by dividing the "w" we computed by

: $w=\frac{2280}{0.175}\frac{radians}{min} \\w=13028.57\,\frac{radians}{min}$

rotational frequency =

$2\pi$

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