Rolling Hoop on Inclined Ramp: Acceleration Calculation

What is the acceleration of the rolling hoop down the inclined ramp?

A thin hoop of mass 3.8 kg and radius 0.2 m rolls down a ramp inclined at an angle 0.45 radians to the horizontal.

Acceleration Calculation

The acceleration of the rolling hoop down the inclined ramp is approximately 1.45 m/s².

When a hoop rolls down an inclined plane, it undergoes both linear and rotational motion. The acceleration can be calculated by considering the forces acting on the hoop. The gravitational force can be decomposed into two components: one parallel to the ramp surface and the other perpendicular to it. The parallel component of the gravitational force provides the acceleration down the ramp, while the perpendicular component contributes to the rotational motion.

The acceleration down the ramp can be determined using the equation: a = g * sin(θ) where g is the acceleration due to gravity (approximately 9.8 m/s²) and (θ) is the angle of the ramp with respect to the horizontal (0.45 radians). Substituting the given values into the equation, we have: a = 9.8 * sin(0.45) ≈ 1.45 m/s²

Therefore, the acceleration of the rolling hoop down the inclined ramp is approximately 1.45 m/s².