Since F is the only net force acting on the two masses, it determines the acceleration of both:

The force F2 acting on the smaller mass may now be determined.

Note that by Newton's third law, the force F2 acts backward on m1. Note that the net force acting on m1 is consistent with the above.

 

Connected Masses

 

The force F is the only net force acting on the system of three masses, which are constrained to accelerate together. Therefore Newton's 2nd law gives the acceleration:

Once the acceleration is determined, the masses may be isolated one by one to determine the tensions T1 and T2.

 

Force on Inclined Mass

 

 

Inclined Pulley

 

 

Atwood's Machine

 

 

Lifting Mass

Though a straightforward application of Newton's second law, many find this problem deceptive. The common misconception which is carried into it is that the tension in the rope must equal the weight of the hanging object. When the mass is accelerated, that is not so. You may change the data and then click on either tension or acceleration in the equation below to calculate its value.

 

 

Friction case

 

 

In the standard model of friction, the frictional resistance is given by the coefficient of friction times the normal force.
For this case the normal force is just the weight of the object .

 

Mass with force at angle

 

 

Force on Two Masses

 

 

Connected Masses

The force F is the only net force acting on the system of three masses, which are constrained to accelerate together. Therefore Newton's 2nd law gives the acceleration:

Once the acceleration is determined, the masses may be isolated one by one to determine the tensions T1 and T2.

 

Mass on Incline with Friction

 

 

Force on Inclined Mass

 

 

 

Inclined Pulley

 

 

 

Horizontal Pulley with Friction

Newton's 2nd Law: Rotation

The relationship between the net external torque and the angular acceleration is of the same form as Newton's second law and is sometimes called Newton's second law for rotation. It is not as general a relationship as the linear one because the moment of inertia is not strictly a scalar quantity. The rotational equation is limited to rotation about a single principal axis, which in simple cases is an axis of symmetry.

Net external torque = moment of inertia x angular acceleration