Ch 10: Rotational KinematicsWorksheetSee all chapters
All Chapters
Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics

Concept #1: Converting Between Linear & Rotational

Example #1: Length of string rotating point mass

Practice: A disc of radius 10 m rotates around itself with a constant 180 RPM. Calculate the linear speed at a point 7 m from the center of the disc.

Practice: A rock rotates around a light, 4-m long string. The rock is initially at rest, but reaches 150 RPM in 3 seconds. Calculate its tangential acceleration after 3 s. 

BONUS: Calculate its tangential speed after 3 s.

Practice: A 4 m long blade initially at rest begins to spin with 3 rad/s2 around its axis, which is located at the middle of the blade. It accelerates for 10 s. Find the tangential speed of a point at the tip of the blade 10 s after it starts rotating.

Additional Problems
An inelastic string is wrapped tightly around a cylindrical drum of 10 cm radius. If enough string is pulled out to cause the drum to rotate completely twice, how much string, in m, is pulled out?
When leaving the starting line in a race, a cars wheels (45 cm in diameter) spin at an angular acceleration of 60 rad/s2, while the car accelerates linearly at 11.8 m/s2. Do the car's wheels roll without slipping? After 5 s, how fast will the wheels be spinning? How fast will the car be moving after 5 s?
A car’s wheel rotates along the floor without slipping. If the car is moving at 30 m/s, and the wheels are 45 cm in diameter, what is the rotational speed of the wheels?
An ant is walking on a disk of radius 15 cm rotating at an angular speed of 150 rad/s. At the center of the disk, what is the ant’s linear speed? What about at the rim of the disk?
A car moves forward at a speed of 15 m/s. In order for the car to maintain traction, the wheels have to rotate without slipping. What, then, is the linear speed at the bottom of the wheel, where it meets the ground? What is the linear speed at the top of the wheel?
A wheel of radius 0.300 m is mounted with frictionless bearings about an axle through its center. A light rope is wrapped around the wheel around the wheel and a block is suspended from the free end of the rope. When the system is released from rest, the block descends with a constant linear acceleration of 4.00 m/s2. As the block descends, what is the angular acceleration of the wheel (in rad/s2)?