Question

He speeds up very slightly and begins to slide. The coefficient of kinetic friction is μ_k =0.28. What is the new magnitude, in meters per squared second, of his radial acceleration?

a) 0.28 m/s²
b) 9.8 m/s²
c) 9.52 m/s²
d) 0.52 m/s²

Answer 1

To find the angular acceleration when a car decelerates at 7.00 m/s² with tire radius 0.280 m, use the formula angular acceleration = linear acceleration/radius.

The number of revolutions until the car comes to rest is calculated from the initial angular velocity using kinematic equations for rotational motion.

Step-by-step explanation:

The question involves calculating radial acceleration and angular acceleration in the context of a car with tires on a road.

When the car decelerates at a rate of 7.00 m/s², and the tire radius is given as 0.280 m, we can associate linear deceleration with angular deceleration using the formula: angular acceleration = linear acceleration/radius. Similarly, when discussing radial acceleration, this directly pertains to the centripetal acceleration that occurs when an object is in circular motion.

Given the initial angular velocity of the tires at 95.0 rad/s and considering the tires come to rest, the number of revolutions made can be found using kinematic equations for rotational motion such as θ = ω²₀t + (1/2)αt² where θ is the angular displacement, ω²₀ is the initial angular velocity, and α is the angular acceleration.