Anyone working on the Physics 1BA3 hemi-spherical bowl question? I can't figure out the accelerations!

Question is as follows

1. The problem statement, all variables and given/known data

A block slides down a frictionless half-pipe (shown on the back of this page). It is released from rest at the point (2,0).

Determine the velocity, tangential accleration, radial acceleration and angular acceleration when the block goes through angular displacements of 30, 60, 90, 120, 150 and 180 degrees respectively.

On the diagram, draw vectors to scale representing each of the linear quantities.

do we need actual numbers? i can get a few numbers for the easy points (centre, and two sides) but for 30,120,150,60 im confused on numbers

Clearly did this wrong, it's been a while.
Before I lead you down the wrong path...


r = 2 = constant (means forces are balanced in radial direction)

Angular acceleration
a_angular = g*cos(theta)/r

mac why would you use cos(theta) when determining the angular acceleration?

Originally Posted by tamefoxes

mac why would you use cos(theta) when determining the angular acceleration?

draw free body diagram. observe:
m*g*cos(theta) is the tangential component of gravity on block.

so then:
m*g*cos(theta)=m*a_ta ngential=m*r*a_angula r

a_angular=g*cos(theta )/r


for angles 90 to 180, you draw another free body diagram with block on left hand side... then tangential force is
-m*g*cos(theta)

and so on

but i could be wrong

at 180, and 0 there is no radial acceleration right?
and at 90 there is no tangential acceleration right?

Originally Posted by nparekh

at 180, and 0 there is no radial acceleration right?
and at 90 there is no tangential acceleration right?

radial acceleration is always zero,

dr/d(theta) = 0
r=2=constant

block doesn't sink into the wood.