Rolling Hoop on Incline: True or False?

Is it true or false that the hoop will continue rolling up the incline without slipping?

A thin hoop of negligible width is rolling on a horizontal surface at speed v = 3.7 m/s when it reaches a 11° incline.

True or False: The hoop will continue rolling up the incline without slipping.

Answer:

The hoop will continue rolling up the incline without slipping.

Exciting news! The statement is true. When a hoop rolls on an incline without slipping, it means that its linear velocity and angular velocity are related in a specific way. The condition for a hoop to roll without slipping on an inclined plane is given by the equation v = rω, where v is the linear velocity, r is the radius of the hoop, and ω is the angular velocity.

In this case, the hoop is rolling on a horizontal surface at a speed of 3.7 m/s, so we can say that v = 3.7 m/s. As the hoop reaches the 11° incline, it will continue rolling up without slipping if the linear velocity along the incline is equal to the angular velocity. Since the downward force that acts along the incline helps the rotation of the hoop, it will indeed continue rolling up the incline without slipping.