Solving Rotational Motion: Max Speed on Spherical Hill

In summary, the maximum speed a rider can travel on a motorcycle over a spherical hill with a radius of 12 meters is 24 mph or 10.8 m/s in order to remain on the surface of the hill. This is determined by equating the rider's weight to the centrifugal force acting on them due to circular motion.
  • #1
mxer101
3
0
rotational motion??

Homework Statement


A rider rides a motorcycle over a spherical hill with a radius of 12 meters. Show that the max speed cannot exceed 24mph or 10.8 m/s is he is to remain on the surface of the hill


Homework Equations





The Attempt at a Solution


I am not sure which equation to use!
 
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  • #2
What are the forces acting on him when he is on the top of the hill?
 
  • #3
What force keeps him touching the hill?
 
  • #4
the force keeping him on the hill is gravity so would I use g=1/2 dt2?
 
  • #5
If he is to remain on the surface of the hill, his weight must be equal to the centrifugal force acting on him due to his circular motion. Therefore mg = mv^2/r. Find the value of v.
 

FAQ: Solving Rotational Motion: Max Speed on Spherical Hill

What is rotational motion?

Rotational motion is the movement of an object around an axis, such as a spinning top or a planet orbiting around a star. It involves both linear motion, or movement along a straight line, and angular motion, or movement around an axis.

How is rotational motion different from linear motion?

Rotational motion involves movement around an axis, while linear motion involves movement along a straight line. In rotational motion, the distance from the axis of rotation determines the speed of the object, while in linear motion, the distance from the starting point determines the speed.

What is the max speed on a spherical hill?

The maximum speed on a spherical hill occurs when an object is at the bottom of the hill and is just about to start rolling up the other side. This speed is determined by the object's mass, the radius of the hill, and the force of gravity acting on the object.

How is the max speed on a spherical hill calculated?

The max speed on a spherical hill can be calculated using the equation v = √(2gh), where v is the speed, g is the acceleration due to gravity, and h is the height of the hill. This equation assumes that there is no friction or air resistance present.

How can rotational motion be applied in real-life situations?

Rotational motion is present in various real-life situations, such as the rotation of wheels on a car, the spinning of a ceiling fan, and the motion of planets in our solar system. It is also used in engineering and design, such as in the construction of wind turbines and amusement park rides.

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