# Angular acceleration of solid sphere on frictionless yoke unde no slip roll condition

• jvani
In summary, the question is about a 6kg solid sphere rolling on a horizontal surface with a frictionless axle and a rope applying 33N. The problem is to find the acceleration of the center of mass and how it relates to the rotational acceleration. To solve this, we need to identify the forces acting on the sphere, use Newton's 2nd law for both translation and rotation, and apply the condition for rolling without slipping.

## Homework Statement

m=6kg
r=0.18m
Fapp=33N

I'm struggling to understand how to answer this question and correlate the linear force applied to rotation without being given the coefficient of friction causing the rotational motion.

The question states that a solid sphere of 6kg is free to roll on a horizontal surface under no slip conditions. A frictionless axle is run through the middle of the sphere, with a rope thread through it, the rope applies 33N on the sphere, and the sphere starts to rotate without slipping

Any help would be appreciated

Start by identifying the forces acting on the sphere. Then apply Newton's 2nd law to both rotation and translation.

The only forces I can see in the horizontal direction is the force applied of 33N and the force of friction. I'm struggling see how to find the acceleration of the center of the sphere from what was given, and then how the translational acceleration of the sphere correlates to the rotational acceleration explicitly.

jvani said:
The only forces I can see in the horizontal direction is the force applied of 33N and the force of friction.
Right.
I'm struggling see how to find the acceleration of the center of the sphere from what was given,
Apply Newton's 2nd law, as I suggested.
and then how the translational acceleration of the sphere correlates to the rotational acceleration explicitly.
To relate translational and rotational motion, apply the condition for rolling without slipping.

I have the same question, with different numbers. I do not understand which formula I am to use that relates the force applied to both the translational and rotational dynamics. I realize that the tangential acceleration and centre of mass acceleration are the same.

If I say that Fext=ma and then divide by the mass to get the acceleration, and then use the relationship between linear and angular acceleration it does not work.

How do I find the correct acceleration of the centre of mass?

If I say that Fext=ma and then divide by the mass to get the acceleration, and then use the relationship between linear and angular acceleration it does not work.
Make sure you use ƩF = ma. To solve for the acceleration, you'll need to combine two equations: one for translation and one for rotation.

## 1. What is angular acceleration?

Angular acceleration is the rate of change of angular velocity of a rotating object. It is measured in radians per second squared (rad/s^2).

## 2. What is a solid sphere?

A solid sphere is a three-dimensional object with a round shape that has a constant diameter and is made of a uniform material. Examples of solid spheres include a basketball or a marble.

## 3. What is a frictionless yoke?

A frictionless yoke is a device used for measuring the angular acceleration of a solid sphere. It consists of two vertical arms connected by a horizontal bar, and the sphere is placed on top of the horizontal bar. The yoke is designed to minimize any friction or resistance that may affect the rotation of the sphere.

## 4. What does "no slip roll condition" mean?

The "no slip roll condition" refers to the behavior of a solid sphere when it is rolling without slipping on a surface. This means that the point of contact between the sphere and the surface has zero velocity, and the sphere is rotating at a constant angular velocity.

## 5. How is the angular acceleration of a solid sphere on a frictionless yoke under no slip roll condition calculated?

The angular acceleration of a solid sphere can be calculated using the formula α = τ / I, where α is the angular acceleration, τ is the torque applied to the sphere, and I is the moment of inertia of the sphere about its axis of rotation. In the case of a frictionless yoke under no slip roll condition, the torque can be calculated using the formula τ = mgR, where m is the mass of the sphere, g is the acceleration due to gravity, and R is the radius of the sphere. The moment of inertia for a solid sphere is given by I = (2/5) * m * R^2. By substituting these values into the formula for angular acceleration, we can calculate the angular acceleration of the sphere on a frictionless yoke under no slip roll condition.