A disk is rolling without slipping. If its radius is 0.5 m and it has a linear s

₹0.0

Question: A disk is rolling without slipping. If its radius is 0.5 m and it has a linear speed of 2 m/s, what is its angular speed?

Options:

Correct Answer: 4 rad/s

Solution:

Using v = rω, we have ω = v/r = 2 m/s / 0.5 m = 4 rad/s.

A disk is rolling without slipping. If its radius is 0.5 m and it has a linear speed of 2 m/s, what is its angular speed?

A disk is rolling without slipping. If its radius is 0.5 m and it has a linear speed of 2 m/s, what is its angular speed?

Step 1: Identify the formula that relates linear speed (v), radius (r), and angular speed (ω). The formula is v = rω.
Step 2: Rearrange the formula to solve for angular speed (ω). This gives us ω = v / r.
Step 3: Substitute the given values into the formula. Here, v = 2 m/s and r = 0.5 m.
Step 4: Calculate ω by dividing the linear speed by the radius: ω = 2 m/s / 0.5 m.
Step 5: Perform the division: 2 divided by 0.5 equals 4.
Step 6: Conclude that the angular speed (ω) is 4 rad/s.

Rolling Motion – The relationship between linear speed and angular speed for a rolling object, where v = rω.
Angular Speed Calculation – Understanding how to derive angular speed from linear speed and radius.