Question

The diameter of a typical minivan tire is 64.8 cm.a stone is stuck in the tread of the right rear tire. what is the magnitude and direction of the stone's angular velocity vector if the van is travelling at 10.0km/h?

Answer 1

The magnitude of the angular velocity vector of the stone stuck in the minivan tire is approximately 8.57 rad/s, oriented outward from the axle following the right-hand rule.

Step-by-step explanation:

To find the magnitude of the angular velocity vector for a stone in the tire tread of a minivan, we can start by converting the van’s linear speed from km/h to m/s. Since 10.0 km/h is equivalent to approximately 2.778 m/s (calculated as 10.0 km/h × (1000 m/1 km) × (1 h/3600 s)), next we use the relationship between linear (v) and angular velocity (ω) given by v = rω. The stone's angular velocity is in a direction perpendicular to the rotation of the tire, which is typically defined as pointed outwards from the axle of the wheel following the right-hand rule.

Using the diameter of 64.8 cm (which is 0.648 m radius), the angular velocity (ω) can be found using:

ω = v / r

Therefore:

ω = 2.778 m/s / 0.324 m ≈ 8.57 rad/s