6.4.3 Solving Problems Using Newton's Second Law for Rotational Motion

Question 1

Solving Problems Using Newton’s Second Law for Rotational Motion

Answer 1

• The equation is the rotational analogue of .
• Solving rotational dynamics problems using is very similar to solving regular dynamics problems using :
- Pick your sign/direction conventions.
- Draw force diagrams.
- Analyze the forces/torques and qapply Newton’s second law.
- Do some algebra to solve for the answer.

Question 2

A grinding wheel, which is a disk of uniform thickness, has a diameter of 0.016 m and a mass of 2 kg. How large a torque is needed to accelerate it from rest to 120 rad / s in 8 s?

Answer 2

9.6*10^-4 Nm

Question 3

Two masses m1 and m2 hang on a frictionless pulley of mass M. If all the mass of the pulley can be considered to be at its rim, and M = 2m2 = 3m1, what is the acceleration of the masses m2 and m2? The radius of the pulley is r.

Answer 3

g/11

Question 4

Consider t = rF. Which of the following is correct?

Answer 4

Given that you can always chose a plane where both F and r lie, and the axis of rotation is perpendicular to that plane, then the direction of the torque vector is along the axis of rotation, with the sense given by the right-hand rule

Question 5

True or false?
We have developed the concept of torque as the product of the force magnitude and the moment arm, where the moment arm is the perpendicular distance between the line of action (that is, the line along which the force vector lies, or the extension of the force vector) and the origin (the point about which the rotation occurs).

Answer 5

true

Question 6

A net torque of 6.4 m.N is applied to a fixed 0.15 kg solid-disk pully with a diameter of 0.10 m. What is the angular acceleration of the pulley?

Answer 6

3.4*10^4 rad/s^2

Question 7

Which of the following statements concerning work is not correct?

Answer 7

If a constant force is applied while the angle changes by a finite amount, then W = t(theta 2 - theta 1) = t delta theta. This hold unless there is a radical component of the force

Question 8

A cable is wrapped around a uniform solid cylinder with diameter 0.12 m and a mass of 50 kg. It is pivoted so that it can rotate about its axis. The cable is pulled with a force of 9.0 N. Assume that it unwinds without stretching or slipping. What is its acceleration?

Answer 8

0.36 m/s^2

Question 9

A car accelerates uniformly from rest to 20 m / s in 15 s. The wheels have a radius of 0.3 m. What is the angular acceleration of the wheels?

Answer 9

4.43 rad/s^2

Question 10

A Ferris wheel accelerates from rest to an angular speed of 1.50 rad / s in 12.00 s. Approximating the Ferris wheel as a circular disk with a radius of 30.00 m and a mass of 2.00 metric tons, what is the net torque on the wheel?

Answer 10

1.12*10^5 Nm