Question

A uniform disc of mass M=2.0 kg and radius R=0.45 m rolls without slipping down an...

A uniform disc of mass M=2.0 kg and radius R=0.45 m rolls without slipping down an inclined plane of length L=40 m and slope of 30°. The disk starts from rest at the top of the incline. Find the angular velocity at the bottom of the incline.

Homework Answers

Answer #1

here,

mass of disc , m = 2 kg

radius , r = 0.45 m

L = 40 m

theta = 30 degree

let the angular velocity at the bottom of the incline be w

using conservation of energy

(0.5 * I * w^2 + 0.5 * m * v^2) - (0.5 * I * w0^2 + 0.5 * m * u^2) = m * g * (L * sin(theta))

(0.5 * 0.5 * m * r^2 * (v/r)^2 + 0.5 * m * v^2) - (0.5 * I * 0^2 + 0.5 * m * 0^2) = 2 * 9.81 * (40 * sin(30))

0.75 * v^2 = 9.81 * 40 * sin(30)

solving for v

v = 16.2 m/s

the angular velocity of disk at the bottom , w = v /r

w = 16.2 /0.45 rad/s = 35.95 rad/s

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A solid, uniform sphere of mass 2.0 kg and radius 1.7m rolls without slipping down an...
A solid, uniform sphere of mass 2.0 kg and radius 1.7m rolls without slipping down an inclined plane of height 7.0m . What is the angular velocity of the sphere at the bottom of the inclined plane? a) 5.8 rad/s b) 11.0 rad/s c) 7.0 rad/s d) 9.9 rad/s
A 320-N sphere 0.20 m in radius rolls without slipping 6.0 m down a ramp that...
A 320-N sphere 0.20 m in radius rolls without slipping 6.0 m down a ramp that is inclined at 34° with the horizontal. What is the angular speed of the sphere at the bottom of the slope if it starts from rest?
A 350-N sphere 0.20 m in radius rolls without slipping 6.0 m down a ramp that...
A 350-N sphere 0.20 m in radius rolls without slipping 6.0 m down a ramp that is inclined at 25° with the horizontal. What is the angular speed of the sphere at the bottom of the slope if it starts from rest? rad/s
A 340-N sphere 0.20 m in radius rolls without slipping 6.0 m down a ramp that...
A 340-N sphere 0.20 m in radius rolls without slipping 6.0 m down a ramp that is inclined at 34° with the horizontal. What is the angular speed of the sphere at the bottom of the slope if it starts from rest? in rad/s
Suppose a solid sphere of mass 450 g and radius 5.00 cm rolls without slipping down...
Suppose a solid sphere of mass 450 g and radius 5.00 cm rolls without slipping down an inclined plane starting from rest. The inclined plane is 7.00 m long and makes an angel of 20.0 o from the horizontal. The linear velocity of the sphere at the bottom of the incline is _______ m/s. please show work
A solid, uniform disk of radius 0.250 m and mass 54.1 kg rolls down a ramp...
A solid, uniform disk of radius 0.250 m and mass 54.1 kg rolls down a ramp of length 3.80 m that makes an angle of 12.0° with the horizontal. The disk starts from rest from the top of the ramp. (a) Find the speed of the disk's center of mass when it reaches the bottom of the ramp. ___________m/s (b) Find the angular speed of the disk at the bottom of the ramp. ___________rad/s
A thumbtack rolls down an inclined plane without slipping, the motion is similar to a pendulum...
A thumbtack rolls down an inclined plane without slipping, the motion is similar to a pendulum when looking from above. The thumbtack is a disk of mass M and radius R with a massless stem of length L from the center of the disk. The inclined plane has an angle of theta. Write down the Lagrangian for this system and find the angular frequency of oscillation away from the equilibrium position of the thumbtack.
.A uniform sphere of mass m radius r starts rolling down without slipping from the top...
.A uniform sphere of mass m radius r starts rolling down without slipping from the top of another larger sphere of radius R. Find the angular velocity of the sphere after it leaves the surface of the larger sphere.
Problem 4 A hoop and a solid disk both with Mass (M=0.5 kg) and radius (R=...
Problem 4 A hoop and a solid disk both with Mass (M=0.5 kg) and radius (R= 0.5 m) are placed at the top of an incline at height (h= 10.0 m). The objects are released from rest and rolls down without slipping. a) The solid disk reaches to the bottom of the inclined plane before the hoop. explain why? b) Calculate the rotational inertia (moment of inertia) for the hoop. c) Calculate the rotational inertia (moment of inertia) for the...
A solid cylinder rolls without slipping down a 30° incline that is 5.0 m long. The...
A solid cylinder rolls without slipping down a 30° incline that is 5.0 m long. The cylinder's mass is 3.0 kg and its diameter is 44 cmcm . The cylinder starts from rest at the top of the ramp. 1) What is the linear speed of the center of the cylinder when it reaches the bottom of the ramp. 2) What is the angular speed of the cylinder about its center at the bottom of the ramp. 3) What is...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT