Rotational Motion Facts Review

​ (a)   θ indicates the angle through which an object has rotated.  It is measured in radians.

• Angular Displacement
• Average Angular Velocity
• Instantaneous Angular Velocity
• Angular acceleration

Answer explanation

Angular displacement θ indicates the angle through which an object has rotated.  It is measured in radians.

​ (a)   ω is angular displacement divided by the time interval over which that angular displacement occurred.  It is measured in rad/s.

• Average angular velocity
• Instantaneous Angular Velocity
• Angular acceleration
• Angular Displacement

Answer explanation

Average angular velocity ω is angular displacement divided by the time interval over which that angular displacement occurred.  It is measured in rad/s.

​ ​ ​ (a)   is how fast an object is rotating at a specific moment in time.​

• Instantaneous angular velocity
• Average Angular Velocity
• Angular acceleration
• Angular Displacement

Answer explanation

Instantaneous angular velocity is how fast an object is rotating at a specific moment in time.

​ (a)   α tells how much an object’s angular speed changes in one second.  It is measured in rad/s per second.​

• Angular acceleration
• Average Angular Velocity
• Instantaneous Angular Velocity
• Angular Displacement

Answer explanation

Angular Acceleration α tells how much an object’s angular speed changes in one second.  It is measured in rad/s per second.

​ (a)   changes an object’s rotational speed, while ​ (b)   changes an object’s direction of motion.

• Angular Acceleration
• Centripetal Acceleration

Answer explanation

Angular acceleration and centripetal acceleration are independent. Angular acceleration changes an object’s rotational speed, while centripetal acceleration changes an object’s direction of motion.

What variable links linear and rotational motion?

• time

• radius

• mass

• speed

Answer explanation

The linear displacement of a rotating object is given by rθ, where r is the distance from the rotational axis.

The linear speed of a rotating object is given by v = rω

The linear acceleration of a rotating object is given by a = rα.

Match the following

• v

• Vf=Vo+at

• x

• F=ma

• a

Answer explanation

Relationship between angular and linear motion

The linear displacement of a rotating object is given by rθ, where r is the distance from the rotational axis.

The linear speed of a rotating object is given by v = rω

The linear acceleration of a rotating object is given by a = rα.

Rotational kinematics -- Equations

The constant-acceleration kinematics equations for rotation are essentially identical to those for linear motion:

Match the following

• angular displacement

• torque

• angular velocity

• moment of inertia

• angular acceleration

The torque provided by a force is given by τ = Fd⊥ , where d⊥ refers to the “_____ ___.”

Answer explanation

The torque provided by a force is given by τ = Fd⊥ , where d⊥ refers to the “lever arm.”

​ (a)   : the closest distance from the pivot, fulcrum, or axis of rotation to the line of which the force acts.

​ (b)   : the line through the point at which the force is applied.

• Lever arm
• Line of Action

Answer explanation

Lever arm: the closest distance from the pivot, fulcrum, or axis of rotation to the line of which the force acts.

Line of Action: the line through the point at which the force is applied.