Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
1 / 4
This page cannot be seen from the preview
Don't miss anything!
Angular momentum (L) is the tendency to continue rotating at the same speed along the same axis. Angular momentum is a vector. Points in the same direction as angular velocity. Units are kg m^2 /s.
Translational Momentum
Torque and Angular Momentum Angular momentum of an object or system is changed by a net torque. Change in angular momentum is called angular impulse. Newton’s Second Law (momentum version) Impulse-Momentum Theorem 𝐹⃗ =
Translational ∆𝑝⃗= 𝐹⃗ ∆𝑡 𝜏⃗=
Rotational ∆𝐿 = 𝜏⃗∆𝑡 A wheel with radius 0.33 m and rotational inertia 2.0 kg m^2 spins on an axle with an initial angular speed of 3.0 rad/s. Friction in the axle exerts a torque on the wheel, causing the wheel to stop after 6.0 s. Calculate the magnitude of the average torque exerted on the wheel as it slows down. A bicycle wheel of known rotational inertia is free to rotate about its central axis. With the wheel initially at rest, a student wraps a string around the wheel and pulls the string with a spring scale, causing the wheel to rotate. The student records the tension in the string and the time for which the string was pulled. Without measuring the wheel’s final angular speed, can the student find the magnitude of the wheel’s final angular momentum, and what is a correct explanation? (A) Yes. The student has sufficient information already. (B) Yes. The student also needs to measure the wheel’s radius to calculate the torque exerted on the wheel. (C) No. Angular momentum can only be found by measuring rotational inertia and angular speed. (D) No. Measuring the radius would allow the student to calculate the torque, not the angular momentum.
A rod is at rest on a flat, horizontal surface. One end of the rod is attached to a pivot, and the rod may freely rotate around the pivot if acted upon by a net external torque, as shown in Figure 1. In an experiment, the rod is initially at rest and student exerts a net torque on the rod. Data are collected to create a graph of the rod’s angular acceleration as a function of time, as shown in Figure 2. Frictional forces are considered to be negligible. How can the student use the graph to determine the angular momentum of the rod at 5 s? (A) Determine the average angular acceleration from 0 s to 5 s and multiply the result by the rotational inertia of the rod. (B) Determine the area bound by the curve and the horizontal axis from 0 s to 5 s and multiply the result by the rotational inertia of the rod. (C) Determine the average slope of the curve from 0 s to 5 s and multiply the result by the rotational inertia of the rod. (D) Multiply the angular acceleration at 5 s by the rotational inertia of the rod.
