A bicycle wheel with a radius of 38 cm is given an angular acceleration of 2.61 rad/s2 by applying a force of 0.45 N on the edge of the wheel. What is the wheel's moment of inertia?
To find the wheel's moment of inertia, we can use the formula:
τ = Iα,
where τ is the torque, I is the moment of inertia, and α is the angular acceleration.
First, let's find the torque applied to the wheel:
τ = Fr,
where F is the force applied on the edge of the wheel and r is the radius.
τ = (0.45 N)(0.38 m),
converting the radius from centimeters to meters.
τ = 0.171 N*m.
Now, we can rearrange the formula τ = Iα to solve for the moment of inertia:
I = τ/α.
Plugging in the values we know:
I = (0.171 N*m)/(2.61 rad/s²),
I = 0.0656 kg*m².
Therefore, the wheel's moment of inertia is 0.0656 kg*m².