Question:
A circular disc of radius $ R $ rolls without slipping along the horizontal surface with constant velocity $ v_0 $ . We consider a point $ A $ on the surface of the disc. Then the acceleration of the point $ A $ is :
A circular disc of radius $ R $ rolls without slipping along the horizontal surface with constant velocity $ v_0 $ . We consider a point $ A $ on the surface of the disc. Then the acceleration of the point $ A $ is :
Updated On: Jun 20, 2022
- constant in magnitude as well as direction
- constant in direction
- constant in magnitude
- constant
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The Correct Option is A
Solution and Explanation
The circular disc of radius $R$ rolls without slipping. Its centre of mass is $C$ and $P$ is point
where body is in contact with the surface at any instant. At this instant, each particle of body is moving at right angles to the line which joins the particle with point $P$ with velocity
proportional to distance. In other words the combined translational and rotational motion
is equal to pure rotation and body moves constant in magnitude as well as direction.
where body is in contact with the surface at any instant. At this instant, each particle of body is moving at right angles to the line which joins the particle with point $P$ with velocity
proportional to distance. In other words the combined translational and rotational motion
is equal to pure rotation and body moves constant in magnitude as well as direction.
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Concepts Used:
Centripetal Acceleration
A body that moves in a circular motion (with radius r) at a constant speed (v) is always being accelerated uninterruptedly. Thus, the acceleration is at the right angle to the direction of the motion. It is towards the center of the sphere and that of the magnitude 𝑣2/r.
The direction of the acceleration is extrapolated through symmetry arguments. If it points the acceleration out of the plane of the sphere, then the body would pull out of the plane of the circle.
Read More: Centripetal Acceleration