# a spherical snowball of mass m and radius r starts from rest and rolls without slipping down a roof that makes an angle θ with the horizontal.

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get a spherical snowball of mass m and radius r starts from rest and rolls without slipping down a roof that makes an angle θ with the horizontal. from EN Bilgi.

## A solid sphere of mass m and radius R rolls down an inclined plane from rest without slipping as shown in the figure. What will be the maximum velocity of the sphere when it will reach the ground?

Click here👆to get an answer to your question ✍️ A solid sphere of mass m and radius R rolls down an inclined plane from rest without slipping as shown in the figure. What will be the maximum velocity of the sphere when it will reach the ground?

Question

## A solid sphere of mass m and radius R rolls down an inclined plane from rest without slipping as shown in the figure. What will be the maximum velocity of the sphere when it will reach the ground?

**A**

7 10gh

**B**

7 gh

**C**

3 10gh

**D**

3 gh Hard Open in App Solution Verified by Toppr

Correct option is A)

The loss in gravitational potential energy is equal to the gain in translational kinetic energy and rotational kinetic energy for the case of maximum velocity of sphere when it reaches ground.⟹mgh= 2 1 mv 2 + 2 1 Iω 2 ⟹mgh= 2 1 mv 2 + 2 1 ( 5 2 mR 2 )ω 2

From the no-slip condition:

v=Rω ⟹mgh= 2 1 mv 2 + 10 2 mv 2 ⟹v= 7 10gh

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## Rolling without slipping problems (video)

David explains how to solve problems where an object rolls without slipping.

Current time:0:00Total duration:15:00

Torque, moments, and angular momentum

## Rolling without slipping problems

David explains how to solve problems where an object rolls without slipping. Created by David SantoPietro.

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## Torque, moments, and angular momentum

Introduction to torque

Moments Moments (part 2)

Finding torque for angled forces

Torque

Rotational version of Newton's second law

More on moment of inertia

Rotational inertia

Rotational kinetic energy

Rolling without slipping problems

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Angular momentum

Constant angular momentum when no net torque

Angular momentum of an extended object

Ball hits rod angular momentum example

Cross product and torque

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## Want to join the conversation?

Log in Ninad Tengse 6 years ago

Posted 6 years ago. Direct link to Ninad Tengse's post “At 13:10 isn't the height...”

At 13:10 isn't the height 6m?

• CLayneFarr 6 years ago

Posted 6 years ago. Direct link to CLayneFarr's post “No, if you think about it...”

No, if you think about it, if that ball has a radius of 2m. So when the ball is touching the ground, it's center of mass will actually still be 2m from the ground. It's true that the center of mass is initially 6m from the ground, but when the ball falls and touches the ground the center of mass is again still 2m from the ground. That means the height will be 4m. If you work the problem where the height is 6m, the ball would have to fall halfway through the floor for the center of mass to be at 0 height.

Tuan Anh Dang 4 years ago

Posted 4 years ago. Direct link to Tuan Anh Dang's post “I could have sworn that j...”

I could have sworn that just a couple of videos ago, the moment of inertia equation was I=mr^2, but now in this video it is I=1/2mr^2. Please help, I do not get it.

• Andrew M 4 years ago

Posted 4 years ago. Direct link to Andrew M's post “depends on the shape of t...”

depends on the shape of the object, and the axis around which it is spinning.

ananyapassi123 5 years ago

Posted 5 years ago. Direct link to ananyapassi123's post “At 14:17 energy conservat...”

At 14:17 energy conservation is used which is only applicable in the absence of non conservative forces. However, isn't static friction required for rolling without slipping?

• Johnny Dollard 2 years ago

Posted 2 years ago. Direct link to Johnny Dollard's post “In this case, conservatio...”

In this case, conservation of energy can be used because no energy is lost to friction. The static friction force is actually what causes the object to rotate, so the energy is conserved as rotational kinetic energy.

James 5 years ago

Posted 5 years ago. Direct link to James's post “02:56; At the split secon...”

02:56; At the split second in time v=0 for the tire in contact with the ground. How is it, reference the road surface, the exact opposite point on the tire (180deg from base) is exhibiting a v>0? Surely the finite time snap would make the two points on tire equal in v? Unless the tire is flexible but this seems outside the scope of this problem...

• shreyas kudari 5 years ago

Posted 5 years ago. Direct link to shreyas kudari's post “I have a question regardi...”

I have a question regarding this topic but it may not be in the video. Suppose a ball is rolling without slipping on a surface( with friction) at a constant linear velocity.

We know that there is friction which prevents the ball from slipping. Why doesn't this frictional force act as a torque and speed up the ball as well?The force is present. It can act as a torque.

Also consider the case where an external force is tugging the ball along. In this case, my book (Barron's) says that friction provides torque in order to keep up with the linear acceleration.

In the first case, where there's a constant velocity and 0 acceleration, why doesn't friction provide

torque?

Can someone please clarify this to me as soon as possible?

Thanks a lot!!

#APphysicsCMechanics

• V_Keyd 5 years ago

Posted 5 years ago. Direct link to V_Keyd's post “If the ball is rolling wi...”

If the ball is rolling without slipping at a constant velocity, the point of contact has no tendency to slip against the surface and therefore, there is no friction. If the ball were skidding and rolling, there would have been a friction force acting at the point of contact and providing a torque in a direction for increasing the rotational velocity of the ball. This increase in rotational velocity happens only up till the condition V_cm = R.ω is achieved. So friction force will act and will provide a torque only when the ball is slipping against the surface and when there is no external force tugging on the ball like in the second case you mention.

In the second case, as long as there is an external force tugging on the ball, accelerating it, friction force will continue to act so that the ball tries to achieve the condition of rolling without slipping.

Anjali Adap 5 years ago

Posted 5 years ago. Direct link to Anjali Adap's post “I really don't understand...”

## Solved A spherical snowball of mass M and radius R starts

Answer to Solved A spherical snowball of mass M and radius R starts

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Guys, does anyone know the answer?