Pseudo Forces on a Mass in a Groove on a Rotating Disc

[Manish_529]

Homework Statement

A block is placed in a groove along the diameter of a circular disc of radius 'R' the disc is rotating with an angular velocity 'w' comment on the velocity of the block.

Relevant Equations

F=ma

Now, I can calculate the velocity of the block using the concept of pseudo force (which here is the centrifugal force), and newton's second law i.e F=ma but, I don't understand why should this block move I mean in the non-inertial reference frame the reason can be given by the centrifugal force, but what explains it's motion in an inertial reference frame because there no forces are acting on the block along the groove so it shouldn't be moving and yet it does how? (A similar situations picture has been attached for reference.)

 

[jbriggs444]

what explains it's motion in an inertial reference frame because there no forces are acting on the block along the groove so it shouldn't be moving and yet it does how? (A similar situations picture has been attached for reference.)

There is a real tangential force acting on the ball as it travels outward along the groove. There must be because its tangential velocity is clearly increasing.

Have you heard of Coriolis? In the non-inertial frame, the real force cancels Coriolis and the tangential velocity remains constant at zero. In the inertial frame, the real force is unresisted and tangential velocity increases.

 

[DaveC426913]

In the inertial frame, the block simply wants to travel straight.

A straight path brings it to the outer edge.

 

[Orodruin]

Inertia.

The block gets accelerated in the tangential direction by the groove, then the grove rotates which changes which direction is the radial direction.

In other words, let’s say the groove starts out parallel to the y axis. As it starts rotating it gives the block some velocity in the x direction. As it rotates, it is no longer parallel to the y axis but develops an non-zero component in the x direction, in which the block is moving.

 

[kuruman]

There has been considerable discussion on this that started a bit more than a year ago and went on for about three months and a total of 155 posts until it was closed by the mentors. See https://www.physicsforums.com/threa...outward-when-opening-the-fridge-door.1057040/

You are welcome to slog through all the replies. My contributions were post #13 which addresses your question in very general terms and post #74 (https://www.physicsforums.com/threa...d-when-opening-the-fridge-door.1057040/page-3) in which I solve for the trajectory in the inertial frame of an object such as you describe. I will not repeat myself here.

 

[gleem]

If a constant force acts on a moving object such that it is always perpendicular to the motion the object will move in a circle of constant radius. In order for the block to remain in the groove a force must be present acting radially on the block just large enough to change its direction at a rate depending on the distance the object is from the center of rotation. This force could be friction or a mechanical restrain. If this force is not large enough then the block will continue to slide outwardly until whatever force is present is enough to cause the rate of change in direction.

Similarlly when you are a passenger in a car travely down Main street at 40 miles per hour and the car makes a quick left turn you tend to want to continue to move down main street but are forced to change your direction by the door pushing on you or the friction of the seat trying to keep you in the car. If these restraints where not there you would have continued down Main street at 40 miles per hour.