Question

In accelerated pure rolling ,as we know velocity of the bottom most point is zero with respect to ground but what makes it to have zero tangential acceleration. If tangential acceleration is to be zero at that point ,it must have net force zero in horizontal direction.The ground applies friction on bottom most point, which in turn applies some internal force on oher points in the body(due to rigidity of body) causing the whole body to get angular acceleration ,the other points applies the same reaction force on the bottom most point .We don't know the magnitude of internal forces. So on what basis we say that these forces cancel each other to make the tangential acceleration or horizontal acceleration of the point zero?

A) The ground applies frictional resistance at that point, yes. But since the wheel (let's say car) isn't slowing down, the transmission is applying torque through the axle, which becomes an equal and opposite force at the wheel: No acceleration, no force (tangentially speaking). B) The ground applies friction on bottom most point
Maybe it does, maybe it doesn't. If the translational and rotational velocities match exactly, no friction will arise.
If there is drag on the object so that it is decelerating, then there will be tangential acceleration on the bottom point.
I think a confusing point is bringing in the real-world. It may help to just imagine the acceleration on an abstract wheel rotating at uniform speed, and then transform to a frame that matches the situation. It's clear that velocity at a point goes to zero, and the acceleration at that point is entirely radial.
At least that works for me.
C) One way to deal with the problem is to work in a frame that moves with the wheel.
From that frame, the tangential velocity of the wheel at the contact point matches the velocity of the ground. The relative velocity is zero.
If the car (I suppose the wheel attached to a car) is accelerating, the equation F=ma
is no longer valid (in that accelerated frame). There is a force from the ground to the wheel but no acceleration, in the same way that someone inside the car feel a force from the seat on his back without accelerates with respect to the car. D) none of these

Answer 1

The bottommost point of a wheel during accelerated pure rolling has zero tangential acceleration due to the opposite forces of friction and internal forces within the wheel canceling out. This occurs even as the wheel itself accelerates, with friction enabling angular acceleration without slipping.

Step-by-step explanation:

In the context of accelerated pure rolling, the bottommost point of the wheel has zero tangential acceleration despite the ground applying friction.

This is because, while the wheel is accelerating, all the internal forces within the rigid body of the wheel - due to rigidity and the application of torque - act in such a way that they cancel out horizontally at the point of contact with the ground. The internal force distribution within the wheel ensures that the bottommost point has no tangential acceleration, as it is instantly balanced by the equal and opposite friction force applied by the ground.

When a car accelerates, the force of friction from the ground is what allows the wheel to gain angular acceleration without slipping. This force, combined with the rolling condition, ensures that the linear acceleration of the car's center of mass matches the angular acceleration around the wheel's axis times the wheel's radius.

Newton's second law, in its rotational form, states that the angular acceleration of a body is directly proportional to the net external torque and inversely proportional to its moment of inertia.

In cases where the car is moving at a constant velocity or is parked, no net force and no net torque mean no acceleration, but when accelerating, the picture changes, and we establish the frictional force as the cause of angular acceleration.