How much torque is applied to a bicycle wheel whose radius is 0.40 m in order to accelerate the 15 kg bike and 78 kg rider at a rate of 3.4 m/s^2?
I'm totally lost on this one. Which equation do I need to use?
Ignore the moment of inertia of the wheel.
F=ma solve for F
Now that F must come from the wheel-ground connection, and Torque/radius=forceatground
Torque=ma/r
To solve this problem, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration:
Force = mass * acceleration
In this case, we want to find the torque applied to the bicycle wheel. Torque is related to force by the equation:
Torque = force * radius
We can rearrange Newton's second law equation to solve for force:
Force = mass * acceleration
Now, we can substitute this expression for force in the torque equation:
Torque = (mass * acceleration) * radius
Now we can plug in the known values:
mass = 15 kg (mass of the bike)
acceleration = 3.4 m/s² (rate of acceleration)
radius = 0.40 m (radius of the bicycle wheel)
Torque = (15 kg * 3.4 m/s²) * 0.40 m
Calculating this expression:
Torque = 204 kg·m²/s² * 0.40 m
Torque = 81.6 kg·m²/s²
So, the torque applied to the bicycle wheel is 81.6 kg·m²/s².