You are holding the axle of a bicycle wheel with radius 35 cm and mass 1 kg. You get the wheel spinning at a rate of 55 rpm and then stop it by pressing the tire against the pavement. You notice that it takes 2.0 s for the wheel to come to a complete stop. What is the angular acceleration of the wheel? (Enter the magnitude.)
To find the angular acceleration of the wheel, we can use the formula:
angular acceleration = (final angular velocity - initial angular velocity) / time
First, let's convert the given initial angular velocity from rpm (revolutions per minute) to radians per second. Since 1 revolution is equal to 2π radians, we can use the conversion factor:
initial angular velocity = (55 rpm) * (2π rad/rev) * (1 min/60 s) = (55 * 2π) / 60 rad/s
Next, we need to find the final angular velocity. Since the wheel comes to a complete stop, the final angular velocity is 0 rad/s.
Plugging in the values, we have:
angular acceleration = (0 rad/s - [(55 * 2π) / 60 rad/s]) / 2.0 s
Simplifying the equation:
angular acceleration = (-[(55 * 2π) / 60] rad/s) / 2.0 s
Calculating this expression gives us the angular acceleration of the wheel.