A garden strimmer uses a piece of string rotating at 100rev s^-1 to trim grass. If the length is 15cm calculate the instantaneous velocity at the end of the chord.
A garden strimmer uses a piece of string rotating at 100rev s^-1 to trim grass. If the length is 15cm calculate the instantaneous velocity at the end of the chord.
Thanks
You know that the linear velocity is the distance covered in time, v=(2*pi*R)/T, where 2*pi*R is the circular distance (circumference), R is the radius of the orbit and T is the time period (time taken for one rotation). Since the angular velocity is w=theta/t (where theta is the angle travelled in radians and t is the time taken to travel that angle), or w=(2*pi)/T, the above equation becomes v=wR so you can simply substitute the numbers into the equation.
You know that the linear velocity is the distance covered in time, v=(2*pi*R)/T, where 2*pi*R is the circular distance (circumference), R is the radius of the orbit and T is the time period (time taken for one rotation). Since the angular velocity is w=theta/t (where theta is the angle travelled in radians and t is the time taken to travel that angle), or w=(2*pi)/T, the above equation becomes v=wR so you can simply substitute the numbers into the equation.
Note that 1 revolution is 2pi radians.
Thanks alot mate, could you also help with this?
A fairground round makes 9revs per minute. What is the angular speed?
A fairground round makes 9revs per minute. What is the angular speed?
I gave you the angular velocity formula as w=theta/t (although you might have seen the equation as w=(2pi)/T, the other equation is a shortcut), so you just need to work out the angular distance, that is 9*2pi, and the time taken for it, that is 1minute*60)
I gave you the angular velocity formula as w=theta/t (although you might have seen the equation as w=(2pi)/T, the other equation is a shortcut), so you just need to work out the angular distance, that is 9*2pi, and the time taken for it, that is 1minute*60)