Force and Motion Dynamics

A particle is moving in a circle with a radius of 2 meters. Its speed increases from 4 m/s to 6 m/s in 0.5 seconds. What is the magnitude of its tangential acceleration?

An object is moving in a circle of radius 5 meters with a constant speed of 10 m/s. What is the magnitude of its centripetal acceleration?

A particle is moving in a circle with a non-constant speed. At a certain instant, its velocity is $v$ and the radius of the circle is $r$. If at this instant, the particle's tangential acceleration is equal to its centripetal acceleration, what is the magnitude of the total acceleration?

A car is making a turn on a flat, horizontal road. Which force provides the centripetal acceleration?

A roller coaster car is at the top of a vertical loop. If the radius of the loop is 10 meters, what is the minimum speed required for the car to stay on the track?

A car is moving at a constant speed around a circular track. What is the direction of the car's centripetal acceleration?

A car is moving around a banked curve with friction. The curve has a radius $r$, and the banking angle is $\theta$. The coefficient of static friction between the tires and the road is $\mu_s$. What is the expression for the maximum speed the car can have without slipping?

What is the primary difference between tangential and centripetal acceleration?

An object is moving in a circle. Its centripetal acceleration is 3 m/s² and its tangential acceleration is 4 m/s². What is the magnitude of the net acceleration?

A particle moves in a circle of radius $r$ with centripetal acceleration $a_c$ and tangential acceleration $a_t$. Find the angle $\theta$ that the total acceleration vector makes with the radial direction.