Rolling Motion Basics
For a wheel rolling smoothly without slipping, this equation relates the speed of the center of mass to the angular speed.
What is v_com = ωR?
The two types of kinetic energy possessed by a smoothly rolling object.
What are translational and rotational kinetic energy?
In three dimensions, torque is defined as the cross product of these two vectors.
What are the position vector and the force vector?
The angular momentum of a particle is the cross product of its position vector and this vector.
What is linear momentum?
This quantity is conserved when the net external torque on a system is zero.
What is angular momentum?
For a rolling wheel, the point of contact with the ground has this instantaneous speed.
What is zero?
For an object rolling down a ramp, this force is responsible for causing the object to rotate.
What is static friction?
The direction of the torque vector is found using this rule.
What is the right-hand rule?
For a rigid body rotating about a fixed axis, angular momentum equals this product.
What is I times ω?
When an ice skater pulls in her arms, her rotational inertia decreases, causing her angular speed to do this.
What is increase?
When viewing rolling motion as pure rotation about the point of contact, the angular speed of the wheel is this compared to the angular speed about its center.
What is the same?
If you increase the mass of a solid sphere rolling down an incline, its acceleration does this.
What is stays the same?
The magnitude of torque can be written as r times F times this trigonometric function of the angle between r and F.
What is sine?
The SI unit of angular momentum.
What is kg·m²/s?
In a tour jeté, a ballet dancer increases rotation speed by decreasing this property.
What is rotational inertia (or moment of inertia)?
A point on the very top of a rolling wheel moves at this speed relative to the center of mass speed.
What is twice the center of mass speed (2v_com)?
The term in the denominator of the rolling acceleration formula that accounts for the distribution of mass.
What is rotational inertia (or I_com)?
A torque that tends to cause a counterclockwise rotation points in this direction relative to the plane of rotation (using the right-hand rule).
What is out of the page?
The direction of the angular momentum vector for a particle moving in a straight line past an origin is determined using this mathematical operation.
What is the cross product?
The reason a spinning gyroscope precesses instead of simply falling over when supported at one end.
What is the torque due to gravity changes the direction of angular momentum, not its magnitude?
The curve traced out by a point on the rim of a rolling wheel.
What is a cycloid?
When a yo-yo rolls down its string, its acceleration can be found using the same formula as a wheel rolling down a ramp with this incline angle.
What is 90 degrees?
The torque due to a force is zero when the force vector is this relative to the position vector.
What is parallel (or anti-parallel)?
A particle moving in a straight line can still have angular momentum about an origin if its velocity vector does this relative to the position vector.
What is does not point directly toward or away from the origin?
When a diver tucks into a ball, her rotational speed increases because her moment of inertia decreases, but this quantity remains constant.
What is angular momentum?