Torque and Rotational Motion AP Physics 1

Angular Kinematics

Discussion Questions How do we get around? How do we move things?

Angular Displacement We’ve discussed linear motion, but what happens when things roll or rotate? If we look at a wheel, how far will it travel linearly in one rotation? Imagine we took the tire off the wheel and stretched it out long!

Angular Displacement Δθ r

Angular Displacement

Angular Velocity

Angular Acceleration

Comparison of linear and angular quantities Linear QuantityAngular Quantity Displacement, xAngular Displacement, θ Converting between linear and angular quantities

Comparison of linear and angular kinematic formulas Linear QuantityAngular Quantity

Torque

Discussion Questions What causes things to rotate? How do you get things to rotate faster or slower?

Torque

F r

F r45°

Torque What happens when multiple forces act on an object? What happens when multiple torques act on an object? When dealing with multiple torques, make sure it is clear where your axis of rotation is since this is how r is measured. FaFa FfFf FNFN FgFg r

Equilibrium Is the box below in translational equilibrium? YES! Is it in rotational equilibrium? NO! It will rotate clockwise. 5N

Torque and Static Equilibrium

A child is sitting on a swing. If the child has a mass of 30 kg, what must the forces in the left and right chains be to hold up the child. The swing seat is 0.5 meters long and of negligible mass. Assume the child’s weight is at the center mass of the swing. FRFR FLFL FgFg R r

Torque

Rotational Inertia or Moment of Inertia If you remember inertia is an object’s resistance to change. It is directly proportional to mass. An object’s rotational inertia or moment of inertia is the object’s resistance to rotations. These are impacted by the size, shape and axis of rotation of the object. I=Ʃmr 2 for systems of particles I=kmr 2 for continuous objects, where k is a constant (usually a fraction) You will NOT need to memorize the moment of inertia for specific objects.

Common Moments of Inertia

Torque

Angular Momentum

Conservation of Angular Momentum If no net external torques act on a system then the system’s angular momentum, L, remains constant.

Angular Momentum An ice skater begins a spin with his arms out. His angular velocity at the beginning of the spin is 2.0 rad/s and his moment of inertia is 6 kgm 2. As the spin proceeds he pulls in his arms decreasing his moment of inertia to 4.5 kgm 2. What is the angular velocity after pulling in his arms? 2.67 rad/s AP Physics C- Rotational Motion- Part II; Dolores Gende