Question

Consider a tire ( 35 kg, and radius of 0.9 m ) that is being held above the ground and spinning at a speed of 20rad/s. The tire is then lowered and held against the ground using its own weight but it does not translate forward, it only skids against the ground. Take the coefficient of kinetic friction is 0.5 and the coefficient of static friction is 0.7 and approximate the tire as a hoop. What is the initial angular momentum of the tire?

Answer 1

The initial angular momentum of the tire, approximated as a hoop, is calculated using the tire's moment of inertia and angular velocity, which results in an angular momentum of 567 kg·m·s^{-1}.

Step-by-step explanation:

To calculate the initial angular momentum of the tire, we use the equation:

L = I × ω

where L is angular momentum, I is moment of inertia and ω is angular velocity.

Since we're approximating the tire as a hoop, the moment of inertia of a hoop is given by:

I = m × r2

where m is mass of the tire (35 kg) and r is the radius of the tire (0.9 m).

Substituting the given values into the equation, we have:

I = 35 kg × (0.9 m)2 = 28.35 kg·m2

Then the initial angular momentum is calculated using the angular velocity (20 rad/s):

L = 28.35 kg·m2 × 20 rad/s = 567 kg·m2/s