Torque with non-perpendicular forces and rotational kinetic energy

[vitaly]

I need some help with these two problems:

1. A wheel of radius 30 cm has forces applied to it as shown in the figure below. Find the torque produced by the force of (a) 4 N (b) 9 N (c) 7 N (d) 6 N. See attachment for figure.
(a) = _____1.2 N*m_____ counterclockwise?
(b) = _____2.7 N*m_____ clockwise?
(c) = __________ N*m
(d) = __________ N*m clockwise
For a, I did: (4N)(.3 M ) = 1.2 N*m
for b, (9 N)(.3 M) = 2.7 N*m
for c, I don't know how to solve it if hte force isn't perpendicular.
for d, same as c. Does anybody know how to solve for c and d, and does anybody know if a and b are correct?

2. A wheel, of mass 6 Kg and radius of gyration 40 cm, is rotating at 300 rpm. Find its momentum of inertia and its rotational KE.
I got:
I = mr^2 = (6 Kg)(0.4 m)^2 = 0.96 kg*m^2. Is that right?
And I'm not sure how to find the rotational kinetic energy. Is there an equation I need?

All help is appreciated. thank you

 

[dextercioby]

For the second,what is the moment of inertia of a disk...?

Daniel.

 

[Wiz]

ke

rotational KE is given by 1/2* I * (w^2)
where I is moment of inertia and w is the angular velocity...
wiz

 

[minger]

Radius of Gyration does not equal the radius of the disk. You will have to find an equation relating mass, Moment of Intertia, and Radius of Gyration. Hint: It involves a division sign and a square root. From there, it is easy to find your Moment of Interia.

To find the rotational interia, it is basically the same equation for linear, but with circular definitions in. (i.e. rad/s instead of m/s, angular velocity instead of linear velocity)

 

[Doc Al]

1. A wheel of radius 30 cm has forces applied to it as shown in the figure below. Find the torque produced by the force of (a) 4 N (b) 9 N (c) 7 N (d) 6 N. See attachment for figure.
(a) = _____1.2 N*m_____ counterclockwise?
(b) = _____2.7 N*m_____ clockwise?
(c) = __________ N*m
(d) = __________ N*m clockwise
For a, I did: (4N)(.3 M ) = 1.2 N*m
for b, (9 N)(.3 M) = 2.7 N*m

Good.

for c, I don't know how to solve it if hte force isn't perpendicular.
for d, same as c. Does anybody know how to solve for c and d, and does anybody know if a and b are correct?

When the force is not perpendicular to the radius, find the component of the force perpendicular to the radius. (Hint: $F sin\theta$, where $\theta$ is the angle that the force makes with the radius.)

a and b are correct.

2. A wheel, of mass 6 Kg and radius of gyration 40 cm, is rotating at 300 rpm. Find its momentum of inertia and its rotational KE.
I got:
I = mr^2 = (6 Kg)(0.4 m)^2 = 0.96 kg*m^2. Is that right?

This is correct.

And I'm not sure how to find the rotational kinetic energy. Is there an equation I need?

$${KE}_{rot} = 1/2 I \omega^2$$
where $\omega$ is the angular speed (measured in radians/sec).