Exploring Rotational Dynamics

What is the formula for torque in terms of force and distance?

• τ = F - r

• τ = F / r

• τ = F + r

• τ = F × r

How does angular acceleration relate to torque and moment of inertia?

• Angular acceleration is independent of torque and moment of inertia.

• Angular acceleration is related to torque and moment of inertia by the equation τ = I * α.

• Moment of inertia has no effect on angular acceleration.

• Torque is equal to the product of angular acceleration and velocity.

Define moment of inertia and its significance in rotational motion.

• Moment of inertia is a measure of an object's resistance to rotational motion, significant for determining angular acceleration under applied torque.

• Moment of inertia is the same as mass in linear motion.

• It measures the speed of an object in circular motion.

• Moment of inertia is irrelevant to torque and angular acceleration.

What factors affect the moment of inertia of an object?

• The temperature of the object

• The speed of the object

• The shape, mass distribution, and distance of mass from the axis of rotation.

• The color of the object

Calculate the moment of inertia of a solid cylinder about its central axis.

• I = m * r^2

• I = (1/2) * m * r^2

• I = (1/3) * m * r^2

• I = (1/4) * m * r^2

What is the expression for rotational kinetic energy?

• KE_rotational = 1/2 mv^2

• KE_rotational = 1/2 Iω^2

• KE_rotational = Iω

• KE_rotational = 2πIω

How does rotational kinetic energy compare to translational kinetic energy?

• Rotational kinetic energy is only relevant for non-moving objects.

• Rotational kinetic energy has no relation to mass or velocity.

• Translational kinetic energy is always greater than rotational kinetic energy.

• Rotational kinetic energy is analogous to translational kinetic energy, but applies to rotating objects.

Explain the principle of conservation of angular momentum.

• Angular momentum can be created or destroyed in any system.

• Angular momentum increases with external forces.

• Angular momentum is only relevant in rotating systems.

• Angular momentum is conserved in a closed system without external torques.

Provide an example of a system where angular momentum is conserved.

• A ball thrown vertically upwards.

• A spinning ice skater pulling in their arms.

• A pendulum swinging back and forth.

• A car moving in a straight line.

What is the relationship between rolling motion and translational motion?

• Rolling motion does not involve rotation.

• Translational motion is a type of rolling motion.

• Rolling motion is a combination of translational and rotational motion.

• Rolling motion is purely translational.