Rotation and Balance
We have 8 ready-to-use problem sets on the topic of Rotational Kinematics, and 14 ready-to-use problem sets on the topic of Rotation and Torque.
The Rotational Kinematic sets focus on the analysis of situations involving a rigid object rotating in either a clockwise or counterclockwise direction about a given point. The object's rotation speed may be increasing, decreasing, or remaining constant.
The Torque and Rotation problems target your ability to use analyze a beam in terms of torque in order to determine the conditions for which it will and will not rotate.
Problem Sets
Set RK1: Determining Angular and Linear Values 1
4 Problems - Medium Difficulty
Given t, r, and 1 other variable for a constantly rotating object, determine all of the remaining angular and linear values.
Set RK2: Determining Angular and Linear Values 2
3 Problems - Medium Difficulty
Given ∆s, ∆θ, and one other variable for a constantly rotating object, determine all of the remaining angular and linear values.
Set RK3: Determining Angular and Linear Values 3
3 Problems - Medium Difficulty
Given tangential velocity, angular speed, and one other variable for a constantly rotating object, determine all of the remaining angular and linear values.
Set RK4: Determining Angular and Linear Values 4
2 Problems - Medium Difficulty
Given angular displacement, angular speed, and one other variable for a constantly rotating object, determine all of the remaining angular and linear values.
Set RK5: Angular Acceleration Problems
6 Problems - Medium Difficulty
Use the definition of angular acceleration to analyze physical situations involving rotation.
Set RK6: Rotational Kinematics Problems Requiring the Big 4
7 Problems - Medium Difficulty
Use kinematic equations for angular quantities to solve rotation problems.
Set RK7: Problems with Segments of Different Angular Acceleration
4 Problems - Very Hard Difficulty
Use rotational kinematic equations to solve problems involving objects undergoing angular accelerations.
Set RK8: Problems with Angular Acceleration and Linear Values
3 Problems - Very Hard Difficulty
Combine an understanding of linear and angular quantities with the use of rotational kinematic equations to analyze complex rotation scenarios.
Set RT1: Torque Produced by a Single Force
6 Problems - Medium Difficulty
Calculate the torque produced by a single force at a set distance from a prescribed pivot point. The angle between the distance and force must be considered. 6 problems.
Set RT2: Torque Produced by One or More Forces
8 Problems - Medium Difficulty
Calculate the torques produced by one or more forces at set distances from a prescribed pivot point. The angles between the distance vectors and forces must be considered. Also calculate the net torque. 8 problems.
Set RT3: Calculating Force to Produce Net Torque = 0, ø = 90˚
6 Problems - Easy Difficulty
Calculate a Force’s magnitude that will create a Net Torque of 0 around a given point. The force makes an angle of 90˚ with the distance vector from the point. 6 problems.
Set RT4: Calculating Force to Produce Net Torque = 0, ø<90˚
6 Problems - Medium Difficulty
Calculate a Force’s magnitude that will create a Net Torque of 0 around a given point. The force makes an angle other than 90˚ with the distance vector from the point. 6 problems.
Set RT5: Beam with mass; Produce Net Torque = 0, ø = 90˚
4 Problems - Easy Difficulty
Calculate a Force’s magnitude that will create a Net Torque of 0 around a given point. The force makes an angle of 90˚ with the distance vector from the point. The weight of the beam needs to be considered. 4 problems.
Set RT6: Beam with mass; Produce Net Torque = 0, ø < 90˚
6 Problems - Medium Difficulty
Calculate a Force’s magnitude that will create a Net Torque of 0 around a given point. The force makes an angle other than 90˚ with the distance vector from the point. The weight of the beam needs to be considered. 6 problems.
Set RT7: Resting Mass on Beam; Produce Net Torque = 0, ø = 90˚
6 Problems - Easy Difficulty
Calculate a Force’s magnitude that will create a Net Torque of 0 around a given point. The force makes an angle of 90˚ with the distance vector from the point. The weight of the beam and supported mass need to be considered. 6 problems.
Set RT8: Resting Mass on Beam; Produce Net Torque = 0; ø<90˚
6 Problems - Medium Difficulty
Calculate a Force’s magnitude that will create a Net Torque of 0 around a given point. The force makes an angle other than 90˚ with the distance vector from the point. The weight of the beam and supported mass need to be considered. 6 problems.
Set RT9: Mass on Beam with Fulcrum; Net Torque =0; ø=90˚
6 Problems - Easy Difficulty
Calculate a Force’s magnitude that will create a Net Torque of 0 on a beam balanced on a fulcrum at the middle of the beam. The force makes an angle of 90˚ with the distance vector from the fulcrum. 6 problems.
Set RT10: Mass on Beam with Fulcrum; Net Torque =0; ø<90˚
6 Problems - Hard Difficulty
Calculate a Force’s magnitude that will create a Net Torque of 0 on a beam balanced on a fulcrum at the middle of the beam. The force makes an angle other than 90˚ with the distance vector from the fulcrum. 6 problems.
Set RT11: Mass on Beam; moving Fulcrum; Net Torque =0; ø<90˚
6 Problems - Hard Difficulty
Calculate a Force’s magnitude that will create a Net Torque of 0 on a beam balanced on a fulcrum other than the middle of the beam. The force makes an angle other than 90˚ with the distance vector from the fulcrum. 6 problems.
Set RT12: Angled Beams Supporting Hanging Mass
6 Problems - Hard Difficulty
Calculate a Tension’s magnitude that will create a Net Torque of 0 on an angled beam that is supporting hanging masses. The mass of the beam needs to be considered. 6 problems.
Set RT13: Scaffold with Resting Masses
6 Problems - Hard Difficulty
Calculate the Tensions in 2 ropes that hold up a scaffold from above. Masses sitting on the scaffold and the mass of the scaffold need to be considered. 6 problems.
Set RT14: Person on Structure in Equilibrium
6 Problems - Very Hard Difficulty
Calculate various values for a person standing on a beam supported at one end by a pin joint and the other end by a rope. Calculate various values for a person on an angled ladder supported at one end by a vertical wall and the other end by friction with the floor. 3 problems for the beam and 3 problems for the ladder.
Set RD1: Determining the Moment of Inertia for a System of Point Masses
4 Problems - Medium Difficulty
Determine the moment of inertia of several oddly-configured objects if given the position of their massive parts relative to an axis of rotation.
Set RD2: Determining the Moment of Inertia for Objects
5 Problems - Easy Difficulty
Use information about objects of a variety of shapes (e.g., solid disk, ring, solid sphere, hollow sphere, solid rod, etc.) to determine their moment of inertia (I).
Set RD3: Determining the Moment of Inertia for a Combination of Objects
5 Problems - Medium Difficulty
Use information about complex objects that can be modeled as a combination of simple objects in order to determine the moment of inertia (I) of the combination.
Set RD4: Determining the Moment of Inertia using the Parallel Axis Theorem
5 Problems - Medium Difficulty
Use the parallel axis theorem to determine the moment of inertia for a simple object when its axis of rotation is not directed through the center of mass.
Set RD5: Combining Torque and Rotational Kinematics 1
7 Problems - Hard Difficulty
Use the concepts of torque, moment of inertia, angular and linear relationships to solve problems.
Set RD6: Combining Torque and Rotational Kinematics 2
7 Problems - Hard Difficulty
Use the concepts of torque, moment of inertia, angular and linear relationships to solve problems.
Set RD7: Rotational Kinetic Energy
9 Problems - Hard Difficulty
Relate the rotational inertia, the angular and linear velocities, and the rotational kinetic energy for a variety of rotational systems.
Set RD8: Angular Momentum
10 Problems - Hard Difficulty