Types of Acceleration in Rotation Practice Problems

A toy car of mass 250 g is rolling on a circular vertical loop of diameter 1.0 m. The friction between the car and the loop is 0.45. At the top of the loop, the speed of the car is 0.25 m/s. Determine the magnitude of the tangential acceleration at the top of the loop.

A physics student launches a ball with an initial angular speed of 85.0 rpm on a flat circular path. The radius of the path is 35 cm. The ball is subject to rolling friction. Calculate the time it will take the ball to come to rest. The coefficient of rolling friction is 0.25.

The speed of a particle rotating in a circle of radius 0.5 m is increased from rest at a constant rate of 0.25 m/s². At time t, the magnitude of the centripetal acceleration equals the magnitude of the tangential acceleration. Determine the time t.

An 850 g toy sled glides in a circle on a bench (µ_k = 0.4) with the help of a 1.50 m long thread. A fan fitted on the toy thrusts air creating a 6.0 N force perpendicularly to the thread. The thread can withstand a force of 90 N before breaking. Starting from rest, determine the number of circles completed by the toy sled before the thread snaps.

A racing kart accelerates from 15 m/s to 20 m/s as it rounds a tight corner on a flat racetrack. The corner is part of a circular arc with a constant radius of 30 meters. Sketch and label the total acceleration, radial acceleration, and tangential acceleration vectors for the kart at the moment it is halfway through the corner.

A bicyclist maintains a constant speed of 20 km/h while cycling along a circular path with a constant radius of 25 meters in a park. Sketch and label the total acceleration, radial acceleration, and tangential acceleration vectors for the bicyclist.

A truck decreases its speed from 70 km/h to 50 km/h as it takes a curved exit ramp off a highway. The ramp curves with a constant radius of 100 meters. Sketch and label the total acceleration, radial acceleration, and tangential acceleration vectors for the truck as it slows down on the exit ramp.

Imagine a drone with mass m flying in a circle of radius r. Its speed changes over time according to $a_{tan}$ = a + bt², where a and b are constants and t is time in seconds. Starting with an initial speed v₀ at t=0, find the formulas for the tangential force ($F_{tan}$ ) and radial force ($F_R$ ) acting on the drone for any time t greater than 0.