physics help please

[ttran01]

im stuck on a few problems.

a 1kg ball of radius 0.5m rolls up along an incline plane (20 degree inclination angle) for 2.5 m and then rolls back to the bottom

what is the total angular displacement
what is the angular velocity at the bottom

a hallow sphere, initially at rest, is rolling without slipping down a ramp of height 2.0m on one end.

what is the final velocity when it reaches the bottom?
what is the length of the ramp if the radius of the sphere is 5cm and it takes 5 seconds to reach the bottom.


any help will be appreciated. thanks

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[future_dr_house]

a 1kg ball of radius 0.5m rolls up along an incline plane (20 degree inclination angle) for 2.5 m and then rolls back to the bottom

what is the total angular displacement
0, it starts at the bottom and ends up there
what is the angular velocity at the bottom
KE = PE
1/2 mv^2 = mgh
1/2 v^2 = gh
v= sqrt(2gh)
h = 2.5 sin (20)
solve for v

a hallow sphere, initially at rest, is rolling without slipping down a ramp of height 2.0m on one end.

what is the final velocity when it reaches the bottom?
same as above
v= sqrt(2gh)
what is the length of the ramp if the radius of the sphere is 5cm and it takes 5 seconds to reach the bottom.
in the first part you found the velocity (m/s) just multiply it by 5 and you have the length

 

[ttran01]

thanks