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A wheel of mass m and radius r is in accelerated rolling motion without slip under a steady axle torque T. If the coefficient of kinetic friction is μ, the friction force from the ground on the wheel is
[1996]
- a)μ mg
- b)T/r
- c)zero
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
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A wheel of mass m and radius r is in accelerated rolling motion withou...
Friction Force on the Wheel in Accelerated Rolling Motion
Friction force on the wheel in accelerated rolling motion can be determined by considering the forces acting on the wheel.
- Forces Acting on the Wheel:
- The forces acting on the wheel include the normal force from the ground, the gravitational force (mg), and the friction force.
- The normal force balances the gravitational force, resulting in no vertical acceleration.
- The friction force acts in the direction opposite to the direction of motion to prevent slipping.
- Acceleration in Rolling Motion:
- In accelerated rolling motion, the torque T provided by the axle causes both translational and rotational motion.
- The acceleration of the center of mass of the wheel is a = rα, where α is the angular acceleration.
- The friction force provides the necessary torque to accelerate the wheel without slip.
- Determination of Friction Force:
- The friction force can be determined using the equation of motion for the wheel.
- The net torque is given by T - rF, where F is the friction force.
- The friction force F can be calculated by equating the net torque to Iα, where I is the moment of inertia of the wheel about its axis of rotation.
- Since the friction force is not directly proportional to the coefficient of kinetic friction μ, it cannot be determined solely based on the given information.
Therefore, the correct answer is option D, "None of these," as the friction force on the wheel in accelerated rolling motion cannot be directly determined without additional information.
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A wheel of mass m and radius r is in accelerated rolling motion without slip under a steady axle torque T. If the coefficient of kinetic friction is μ, the friction force from the ground on the wheel is[1996]a)μ mgb)T/rc)zerod)None of theseCorrect answer is option 'D'. Can you explain this answer?
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