A disk rolls without slipping on a horizontal surface. If its radius is R and it

A disk rolls without slipping on a horizontal surface. If its radius is R and it rolls with a linear speed v, what is the angular speed of the disk?

A disk rolls without slipping on a horizontal surface. If its radius is R and it rolls with a linear speed v, what is the angular speed of the disk?

Correct Answer: ω = v/R

Step 1: Understand that the disk is rolling without slipping, which means there is a direct relationship between its linear speed and angular speed.
Step 2: Identify the variables: the linear speed of the disk is 'v' and the radius of the disk is 'R'.
Step 3: Recall the formula that relates linear speed (v) and angular speed (ω) for rolling without slipping: ω = v / R.
Step 4: To find the angular speed (ω), simply divide the linear speed (v) by the radius (R).

Rolling Motion – The relationship between linear speed and angular speed for an object rolling without slipping.
Angular Speed – The rate of rotation of an object, typically measured in radians per second.
Linear Speed – The speed at which the center of mass of the rolling object moves along a path.