Torque and Rotational Motion HTHS AP Physics 1 M. Dimler

Torque τ = Fd Torque is a force that causes an object to turn Torque - Force directed perpendicular to the “lever arm” of an object that has the ability to rotate the object around a fulcrum or axis. Note: this is usually an easy distance to visualize τ = Fd Units of Torque are the Newton-Meter

Direction of the Torque Vector The Torque vector is perpendicular to both the position vector and the force vector Right Hand Rule: point fingers of your right hand in the direction of r vector (lever arm from center of rotation), and bend your fingers in the direction of the force vector. Your thumb then points in the direction the torque vector. Positive torques cause ccw rotation, negative torques cause cw rotation.

Net Torque When a force is not exactly acting perpendicular to the “lever arm”, it needs to be broken down into x and y components.

Net Torque

Equilibrium Static Equilibrium implies that the net force and the net torque are zero, and the system is at rest. Dynamic Equilibrium implies that the net force and the net torque are zero, and the system is moving at constant translational and rotational velocity Rotational Equilibrium implies that the net torque on an object is zero.

Once around a circle = 360° = 2π radians = 1 revolution = 1 rotation Radians and Degrees Once around a circle = 360° = 2π radians = 1 revolution = 1 rotation

Rotational Kinematics Angular Position Symbol (θ) Units (radians) Formula (θ=s/r) s=θr Angular Displacement Symbol (Δθ) Units (radians/s) Formula (Δθ=θ2-θ1)

Practice Problem A disk can rotate about its central axis like a merry-go-round. Which of the following pairs of values for its initial and final angular positions, respectively, give a negative angular displacement: -3 rad,+5 rad -3 rad, -7 rad 7 rad, -3 rad

Rotational Kinematics Angular Velocity Symbol (ω) Units (radians/sec) Formula (ω=Δθ/Δt) v=ωr Note: Same at any point along disk Angular Acceleration Symbol (α) Units (radians/sec2) Formula (α=Δω/Δt) at=αr and ar=v2/r=ω2r

Practice Problem Find the magnitude of the earth’s angular velocity in radians per second. Then determine the linear speed of an object on the surface of the earth.

Practice Problem A bear rides a unicycle. If the unicycle wheel begins at rest, and accelerates uniformly in a ccw direction to an angular velocity of 15 rpms in a time of 6 seconds, find the angular acceleration of the unicycle wheel.

Practice Problem What is the average angular velocity in the first two seconds? What is the angular acceleration at 4 seconds? What is the angular displacement during the 10 second interval?

AP Physics 1 MC Practice Problem

Center of Mass

Moment of Inertia Derivation of I for a point mass ½mv2 = ½Iω2 v=ωr ½ m(ωr)2 = ½Iω2 ½ mω2r2 = ½Iω2 mr2 = I Note: Units of I are kg∙m2

Moment of Inertia (Rotational equivalent to mass)

Moments of Inertia can be added together to find the Moment of Inertia of a system consisting of two or more objects. ∑I = I1 + I2

AP Physics I MC Practice

AP Physics I MC Practice

Newton’s 2nd Law for Rotation

Sample Problem A 20-kg ladder of length 8m sits against a frictionless wall at an angle of 60°. The ladder just barely keeps from slipping. Draw a FBD of the ladder. Determine the force of friction of the floor on the ladder. Determine the coefficient of friction between the ladder and the floor.

AP MC Practice Problem

AP Physics I MC Practice

Toilet Paper Roll Drop

Parallel Axis Theorem

Rotational Kinetic Energy

Conservation of Energy

Angular Momentum Angular Momentum is a measure of how difficult it is to stop an object when rotating. Units of Angular Momentum: kg∙m2/s

Angular Momentum L = r x m x v The angular momentum of a point mass can be found by multiplying the linear momentum of the point mass (p=m x v) by the perpendicular distance from axis of rotation to the point mass (r). L = r x m x v

Conservation of Angular Momentum

Angular Impulse

Bozeman Science Videos http://www.bozemanscience.com/ap-physics Click on the link above and watch the following videos. Torque Rotational Motion Angular Momentum Vector Properties of Angular Quantities Angular Impulse Conservation of Angular Momentum Rotational Inertia

Aplusphysics.com Video Lessons http://www.aplusphysics.com/courses/ap-1/AP1_Physics.html#ap1 Click on the link above and watch the following videos. Rotational Kinematics Torque Rotational Dynamics Angular Momentum Rotational Kinetic Energy

Twu Videos https://www.youtube.com/playlist?list=PLUn4SDRnHn7cpTOIptsleLOSwhj4as8vm There are 52 videos on the Rotational Motion playlist. They are relatively short videos, so you should watch all 52 videos prior to next Unit test. You will be quizzed twice a week to ensure you are pacing yourself.