Angular Impulse Calculation with Impact Wrench
How can we calculate the angular impulse imparted to the lug nut by the impact wrench?
Given data: A slender 1-kg rod AB with cylindrical end weights at A and B, each having a diameter of 20 mm and a mass of 1 kg. The rod is given an angular velocity of 4 rad/s and strikes the bracket C without rebounding.
Calculating Angular Impulse Imparted by the Impact Wrench
The angular impulse imparted to the lug nut can be calculated by finding the change in angular momentum. This change is equal to the product of the moment of inertia and the change in angular velocity.
To determine the angular impulse imparted to the lug nut by the impact wrench, we need to calculate the change in angular momentum. The angular impulse is equal to the change in angular momentum. Angular momentum is the product of moment of inertia and angular velocity.
First, we need to calculate the moment of inertia of the system. The moment of inertia of a rod rotating about one of its ends is given by the formula I = (1/3) * M * L^2, where M is the mass of the rod and L is its length. In this case, the mass of the rod is 1 kg and the length is 580 mm (0.58 m), so the moment of inertia of the rod is (1/3) * 1 kg * (0.58 m)^2.
Next, we need to calculate the change in angular velocity. The angular velocity of the rod before it strikes the bracket C on the handle is 4 rad/s, and after the impact, it becomes 0 rad/s. Therefore, the change in angular velocity is -4 rad/s.
Finally, we can calculate the angular impulse by multiplying the moment of inertia by the change in angular velocity. The angular impulse is equal to (1/3) * 1 kg * (0.58 m)^2 * (-4 rad/s).